Free Essay

Exploring Averages

In:

Submitted By lucknicole
Words 1569
Pages 7
Quantitative Literacy
Mat143 LN12
Group Black
Nicole Luck
Lisa Becquet
Sandra Soto
Heather Wicker
Jared Gunter

Exploring the Average I. Background Information

* The three most common measures of center:

Mean
The mean is the best-known and most widely used measure of central tendency. It is what most people call the "average." The mean is calculated by adding up all the scores and dividing the result by the number of scores in the distribution.

Median
The median represents the exact middle of a distribution so that half of the cases are above it and half are below it. It is the middle case in a distribution when the scores are arranged in order from lowest to highest.

Mode
The mode is the category or score with the highest frequency in the distribution. In other words, it is the most common score, or the score that appears the highest number of times in a distribution.

* Skewness
A distribution is said to be skewed when the data points cluster toward one side of the scale than the other, creating a curve that is not symmetrical. In other words, the right and the left side of the distribution are shaped differently from each other. There are two types of skewed distributions. A distribution is positively skewed if the scores fall toward the lower side of the scale and there are very few higher scores. Positively skewed data is also referred to as 'skewed to the right' because that is the direction of the 'long tail end' of the chart. A distribution is negatively skewed if the scores fall toward the higher side of the scale and there are very few low scores.

* Mean, median and mode of a frequency distribution:

http://www.youtube.com/watch?v=vqHEFqKU5gQ

* Creating a bar (column) chart using excel:

http://www.youtube.com/watch?v=Ljc9aizzjsM

II. Exploration

A. Imagine that you were interested in studying the annual income of students one year after they have completed their Master of Business Administration (MBA). You collect data from 400 graduates and find that their yearly income ranges from $20,000 to $150,000. The table below summarizes the data that you have collected. Income (thousands) | Frequency | less than 31 | 3 | 31-40 | 50 | 41-50 | 70 | 51-60 | 87 | 61-70 | 70 | 71-80 | 40 | 81-90 | 30 | 91-100 | 20 | 101-110 | 11 | 111-120 | 9 | 121-130 | 5 | 131-140 | 3 | 141-150 | 2 |

1. Construct a bar (column) chart in excel. Insert the graph here.

2. Describe the shape of the distribution.
The distribution is skewed to the right.

3+50+70+87+70+40+30+20+11+9+5+3+2

3. Calculate the mean.
3+50+70+87+70+40+30+20+11+9+5+3+2= 400/ 13 = 30.8 or 31

4. Estimate the median.
3, 50, 70, 87, 70, 40, 30, 20, 11, 9,5 3, 2 The median is 30

5. Estimate the mode.
The mode is 3 and 70

6. Is the mean greater than, less than, or equal to the median? Explain why this is true.
The mean is just slightly more than the median but only by a little bit. I think this is because the date was skewed towards the right, which is what typically tends to happen.

7. What is the value of the mode in relation to the mean and median?
It represents the group that had the lowest frequency. This would be correct because bar graphs that tend to be skewed to the right, the mode tends to be less than the mean and the median.

8. What can you conclude about the annual income of students one year after they have completed their MBA?
That most tend to earn their income in the 31k to 50k range after they have completed their MBA, earning them a better living and more positive aspect on life.

B. Let's say you are also interested in examining the number of applications each graduate completed before they found their current job. Using data collected from the same 400 graduates, you find that the number of applications they completed ranges from 1 to 15. The table below summarizes the data that you have collected. Applications Completed | Frequency | 1 | 1 | 2 | 2 | 3 | 2 | 4 | 3 | 5 | 5 | 6 | 8 | 7 | 10 | 8 | 25 | 9 | 40 | 10 | 60 | 11 | 80 | 12 | 70 | 13 | 50 | 14 | 33 | 15 | 11 | | | 1. Construct a bar chart in excel. Insert the graph here.

Series 4 Indicates Frequency(gold) and Series 5 Indicates Applications(blue) completed.

2. Describe the shape of the distribution.
The distribution has one peak ad skewed left.

3. Calculate the mean. 1x1+2x2+3x2+4x3+5x5+6x8+7x10+8x25+9x40+10x60+11x80 +12x70 +13x50 +14x33+15x11
1+2+2+3+5+8+10+25+40+60+80+70+50+33+11 =
4,583
400
=11.46

4. Calculate the median.
1+2+2+3+5+8+10+25+40+60+80+70+50+33+11= 400 (n/2) + 1= (400/2) + 1= 200 + 1= 201 is the median

5. Is the mean greater than, less than, or equal to the median? Explain why this is true.
The mean is less than the median and this is common in charts skewed to the left, or also known as a negative skew.

6. What is the value of the mode in relation to the mean?
The value that is most common in a row of data is the mode. In other words, it is the value with the highest frequency. The modal group in this table is group 11, which had the highest frequency of 80. The mean is also 11.47, making it closely related to the mode.

7. What can you conclude about the number of applications each graduate completed before they found their current job.
I can conclude that while putting in more applications increases your chances of finding a job, it is also situational and all depends on your skills and background.

C. Finally, you would like to study GRE scores of the MBA graduates. GRE scores | Frequency | below 960 | 31 | 960-1059 | 48 | 1060-1159 | 64 | 1160-1259 | 98 | 1260-1359 | 72 | 1360-1459 | 64 | above 1459 | 23 |

1. Construct a bar chart in excel. Insert the graph here.

2. Describe the shape of the distribution.
The shape of distribution is unimodal, having only one peak/mode. It is also right-skewed.

3. Calculate the mean.
1209.167

4. Estimate the median.
1209

5. Estimate the mode.
1359

6. Is the mean greater than, less than, or equal to the median? Explain why this is true.
The mean is greater than the median, because if you add all values and then divide by the amount of values you get the mean, which is 1209.167. The median, however, is the middle value which we find by adding 1159 +1259 = 2418, then divide by two = 1209

7. What can you conclude about GRE scores of the MBA graduates?
Most MBA graduates had scores that were in the middle; less MBA graduates scored low or very high.

III. Extensions
1. Give an example of a distribution that is naturally normally distributed. Explain.
Heights of people and blood pressure measurements. Mean=median=mode, symmetry is about in the center and 50% of values less than the mean and 50% greater than the mean. There is a narrow range.

2. Give an example of a distribution that is naturally skewed left. Explain. The age people die from heart disease. There are far more deaths at older ages than younger so the data is skewed left, with few deaths on left side and more on the right.

3. Give an example of a distribution that is naturally skewed right. Explain.
Number of books read by a 5th grade in a school year. Most will read a moderate amount of books but few will read far more than others. These students will therefore be outliners with high values for the number of books read creating a tail on the right side of distribution.

4. Give an example of a data set where the mode is the only possible measure of center.
Termperature in a given week.

5. What is the best measure of center? Explain .
It really just depends on what you are finding the average of. Mean is good when the numbers have a low variable of change. Median works well when the variable is larger. Mode works well when you want to know what is the most coomon.

6. Suppose there are 7 people who graduate from some university with degrees in communications. They all get jobs, and their salaries are: $27,000 $29,000 $33,000 $34,000 $35,000 $39,000 $5,000,000
What is their “average” salary? Which measure of center did you use? Explain why.

34,000. I used median because the 5,000,000 salary would make the average very high which would be wrong because the majority if these workers make considerably lower than 5,000,00.

What does this saying mean?
“A statistician drowned while crossing a river that was on average six inches deep”.
If they used mean for the average there may had been several deep areas but if the shallow areas were much more common he could have fell into a large hole/deep area of the water.

Similar Documents

Free Essay

Nt1210

...Exploring Why and When to Use Shell Scripts Lab 4.4 Lab 5.1 The condition | True or False | attAverage >= verizonAverage | True | tmobileAverage == 868 | True | verizonAverage < sprintAverage | False | sprintAverage != attAverage | True | attAverage = 1410 • sprintAverage = 795 • tmobileAverage = 868 • verizonAverage = 877 Lab 5.2 The condition | Expected Output | If tmobileAverage > 800 AND verizonAverage > 800 Then Display “Both have average download rates over 800” Else Display “One or both of the averages are less” End If | Both have average downloads rates over 800 | If sprintAverage == 800 Then Display “Sprints download rate is 800” End If | No Output | If attAverage >= 1300 OR tmobileAverage >=900 Display “Select either carrier” End If | Select either carrier | Lab 5.3 Main Module( ) Declare Integer testScore = 0 Declare String category = “ “ Declare String interview = “ “ getScore(testScore) employCat(testScore, category) interviewPoss(testScore, interview) displayInfo(testScore, category, interview) End Main Module getScore(Integer Ref testScore) Display “Enter the test score: ” Input testScore End Module Module employCat(Integer testScore, String Ref category) If testScore >= 85 then category = “Definite” Else if testScore >= 70 and testScore < 85 then category = “Likely” Else if testScore >=60 and...

Words: 255 - Pages: 2

Premium Essay

Sport Obermeyer Case

...RECOMMENDATION #1. Improve the demand forecasts made internally by the Buying Committee in November just before Speculative Production. Instead of using just a simple average of the individual forecasts made by Laura, Carolyn, Greg, Wendy, Tom, & Wally, use a weighted average, with the weights reflecting past accuracy. RECOMMENDATION #2. Obtain market feedback earlier than Las Vegas, thereby converting some Speculative Production to Reactive Production. Sport Obermeyer can invite selected retailers to come in January to Aspen for an all-expenses-paid “Early Order Weekend”, where there is time for a”sneak preview” of the new line, some recreational skiing and socializing, and then the early placement of orders at a discount. To maximize the value of the market feedback, Sport Obermeyer’s “guest list” should include both large and small retailers and both urban and resort retailers. RECOMMENDATION #3. Decrease lead times for both raw materials and finished goods, thereby allowing more time to utilize existing capacity. Since the business strategy should emphasize Dependability more than Cost, lead-times can be reduced using some or all of the following methods: Choose suppliers of raw materials more on the basis of D than C. Expedite orders through information sharing with suppliers. Expedite shipments using faster (but more expensive) shippers. Establish some local (but more expensive) production capacity for “last minute” production. Other ways to reduce lead times...

Words: 416 - Pages: 2

Premium Essay

Sport Obeyemer

...RECOMMENDATION #1. Improve the demand forecasts made internally by the Buying Committee in November just before Speculative Production. Instead of using just a simple average of the individual forecasts made by Laura, Carolyn, Greg, Wendy, Tom, & Wally, use a weighted average, with the weights reflecting past accuracy. RECOMMENDATION #2. Obtain market feedback earlier than Las Vegas, thereby converting some Speculative Production to Reactive Production. Sport Obermeyer can invite selected retailers to come in January to Aspen for an all-expenses-paid “Early Order Weekend”, where there is time for a”sneak preview” of the new line, some recreational skiing and socializing, and then the early placement of orders at a discount. To maximize the value of the market feedback, Sport Obermeyer’s “guest list” should include both large and small retailers and both urban and resort retailers. RECOMMENDATION #3. Decrease lead times for both raw materials and finished goods, thereby allowing more time to utilize existing capacity. Since the business strategy should emphasize Dependability more than Cost, lead-times can be reduced using some or all of the following methods: Choose suppliers of raw materials more on the basis of D than C. Expedite orders through information sharing with suppliers. Expedite shipments using faster (but more expensive) shippers. Establish some local (but more expensive) production capacity for “last minute” production. Other ways to reduce lead...

Words: 303 - Pages: 2

Free Essay

Hawala

...information retrieval systems are based on a number of key premises, including that representative topic sets can be created, that suitable relevance judgements can be generated, and that systems can be sensibly compared based on their aggregate performance over the selected topic set. This paper considers the role of the third of these assumptions – that the performance of a system on a set of topics can be represented by a single overall performance score such as the average, or some other central statistic. In particular, we experiment with score aggregation techniques including the arithmetic mean, the geometric mean, the harmonic mean, and the median. Using past TREC runs we show that an adjusted geometric mean provides more consistent system rankings than the arithmetic mean when a significant fraction of the individual topic scores are close to zero, and that score standardization (Webber et al., SIGIR 2008) achieves the same outcome in a more consistent manner. Keywords: Retrieval system evaluation, average precision, geometric mean, MAP, GMAP. 1 Introduction (or not) that was obtained relative to other previous techniques. A variety of mechanisms have evolved over the years to perform these tasks. For example, because of the high cost of undertaking relevance judgements, steps 1 and 2 have tended to be carried out via large whole-ofcommunity exercises such as TREC and CLEF. To perform step 3, we might build our own software system, or, to again make use of shared resources...

Words: 8460 - Pages: 34

Premium Essay

Servqual for Banking

...Measuring Service Quality Using SERVQUAL |Introduction |Measuring the quality of a service can be a very difficult exercise. Unlike product where there | | |are specific specifications such as length, depth, width, weight, colour etc. a service can have| | |numerous intangible or qualitative specifications. In addition there is there expectation of the| | |customer with regards the service, which can vary considerably based on a range of factors such | | |as prior experience, personal needs and what other people may have told them. | |SERVQUAL – a methodology for |As a way of trying to measure service quality, researchers have developed a methodology known as| |measuring service quality |SERVQUAL – a perceived service quality questionnaire survey methodology. SERVQUAL examines five | | |dimensions of service quality: | | |Reliability | | |Responsiveness | | |Assurance; ...

Words: 1409 - Pages: 6

Free Essay

Course Project B

...paragraphs I have prepared my results of the mean average income, population of urban customers to total customers, number of years customers have lived in their current homes, and average customers credit balance. The first variable I will discuss is the likelihood the average income is less than $50,000. After looking at the sample of the customers I have discovered that the average annual income falls between $39,680 and $47,800. When it was tested further we have strong evidence that the average income for all customers is less than $50,000. The second variable I will discuss is the whether the percentage of urban customers is more than 40%. Initial testing revealed that the percentage of urban customers falls between 30 and 57%. Further testing revealed that we have strong evidence that the percentage of urban customers is greater than 40%. The third variable to be discussed is whether the average years a customer has lived at their current residence is less than 13 years. The mean years a customer has lived at their current residence is between 11 and 14 years. Based on some further testing there is strong evidence that the average number of years is more than 13 years. The fourth and final variable to be discussed is whether the average credit balance for customers is more than $4,300. The average credit balance for customers is between $3,712 and $4,228. Based on the averages we have strong evidence that the average credit balance is not more than $4,300 but actually...

Words: 529 - Pages: 3

Premium Essay

Jet Copies

...Jet Copies Shaneka Thompson Assignment 1 Math 540 Case Problem Finding the average days of repair in the simulation, first you click on the module at the top and scroll to simulation. Click simulation and open new file. There was a pop up box which you label. I labeled mine Average days of repair. Then I picked 4 categories and put in 100 trails and clicked Ok. When the spreadsheet came up I place in the value section 1, 2, 3, 4 and he frequency I placed 0.2, 0.45., 0.25, and 0.10 and clicked solved in the top. This gave me an average of 2.31 days. By hand I calculated the copies per day. I repeated the steps for getting the weeks between break down. I picked 4 categories and 100 trials. For the values I placed in 1, 2, 3, 4 symbolizing the weeks and 1,1,1,1 for the frequency. This simulation gave me the average of 2.68. By hand I calculated the estimated loss of revenue per year. The third simulation was to determine the loss of revenue per day. The values that were used were the estimated dollar amount and the frequency that I used was 1, 1, 1. This gave me an average of 521 days. I then by hand found the estimated revenue lost. Once the average numbers were tallied, I placed the numbers in the stimulation to gather the average cost per year which was by, simulation 23,633. 58 to 23,931.54 and by estimate was 23,100. The overall view the QM simulation if uses correctly and numbers are used correctly gives a correct simulation of loss or profit. I believe just using one...

Words: 577 - Pages: 3

Premium Essay

Pepsi Co Case Study

...Pepsi Co With the assumptions given in the case, we estimated the WACC to be 12.23%. The cost of equity represented in the WACC was calculated using the geometric mean return on T-bonds and the long-term government bond rate (4.5%) as the appropriate risk free rate. We chose this over the arithmetic mean return using T-bills under the assumption that the geometric mean is more appropriate to use in estimating the expected return over longer time horizons, especially because as we go towards longer time horizon returns become more serially correlated. The difference in our estimated WACC from the 11% estimated could be attributed to the choice between arithmetic or geometric risk premiums and the short term/long-term risk free rates. (See exhibit 1) Since PepsiCo is comprised of three different business segment, we felt that it was in our best interest to calculate the cost of capital for each of the segments in order to achieve the appropriate WACC. We calculated the new WACCs via pure play method and used comparable companies for references (See Exhibit 2 for divisional segments). In order to use the pure play method, we averaged the betas, debt-equity ratios, and tax rates for all the related companies in each segment. We unlevered the betas and re-levered it to PepsiCo’s specifications. We arrived with the betas of .85, .83, and 1.19 for restaurants, snack foods, and soft drinks respectively. In the end we estimated 12.17%, 13.15%, and 15.74% as our new WACCs for the divisions...

Words: 455 - Pages: 2

Premium Essay

Psyc 315 Week Two Individual

...12) a) equal-interval (quantitative and the zero is your choice) examples: degrees in Celsius scale or Fahrenheit counting of the years (our position of zero is different from other cultures) b) rank-order (= nominal + natural ranking is available) examples : the size of T-shirts (S, M, L, XL) or the number of stars of a movie c) nominal (everything that can be put into categories is nominal) examples of pure nominal the political party people vote for the color of hair or eyes d) ration (quantitative and the zero means that the thing is not there) example: weight of a pakage, length of a ruler, number of children in a family e)continuous: uncountable 15) Following are the speeds of 40 cars clocked by radar on a particular road in an 35-mph zone on a particular afternoon: 30, 36, 42, 36, 30, 52, 36, 34, 36, 33, 30, 32, 35, 32, 37, 34, 36, 31, 35, 20, 24, 46, 23, 31, 32, 45, 34, 37, 28, 40, 34, 38, 40, 52, 31, 33, 15, 27, 36, 40 Make (a) a frequency table and (b) a histogram. Then (c) describe the general shape of the distribution. (a) Frequency Table SPEED FREQUENCY PERCENTAGE 15-19 1 2.5 20-24 3 7.5 25-29 2 5 30-34 15 37.5 35-39 11 27.5 40-44 4 10 45-49 2 5 50-54 2 5 (b) Histogram (c) The general shape of distribution is unimodal. 19) (a) bimodal is usually a combination of two different distribution, for example heights of people, there is the distribution for men and for women, so if we do not differentiate between...

Words: 632 - Pages: 3

Free Essay

Frequency Distribution

...Frequency Distributions & Sampling 1. Is the lager sampling changing anything? 2. Is your mean increasing or decreasing? 3. Do you think your current data is enough to paint a picture? The increasing of collected data quite fortunately allowed the majority of the data to remain the same. It increased the total drive time 392 total minutes of drive time. However, mean and mode still remained the same with an average of 24.5 minutes (mean) and a reoccurring number of number 22 (mode) which repeats a total of 4 times. Based on the consistency of my data I do believe I have enough information to create an accurate assessment of the collected data. Day | Amount of time it takes to drive to work daily | 1 | 27 minutes | 2 | 29 minutes | 3 | 21 minutes | 4 | 24 minutes | 5 | 22 minutes | 6 | 25 minutes | 7 | 28 minutes | 8 | 22 minutes | 9 | 26 minutes | 10 | 23 minutes | 11 | 22 minutes | | Five additional days of data | 12 | 25 minutes | 13 | 23 minutes | 14 | 22 minutes | 15 | 26 Minutes | 16 | 27 Minutes | | | | | x | f | xf | (x-xbar)^2 | (x-xbar)^2*f | 1 | 27 | 27 | 55.443 | 1496.9587 | 2 | 29 | 58 | 41.551 | 1204.9766 | 3 | 21 | 63 | 29.659 | 622.8372 | 4 | 24 | 96 | 19.767 | 474.4060 | 5 | 22 | 110 | 11.875 | 261.2482 | 6 | 25 | 150 | 5.983 | 149.5729 | 7 | 28 | 196 | 2.091 | 58.5456 | 8 | 22 | 176 | 0.199 | 4.3762 | 9 | 26 | 234 | 0.307 | 7.9798 | 10 | 23 | 230 | 2.415 | 55.5431 | 11 | 22...

Words: 322 - Pages: 2

Premium Essay

Acl Ch. 4

...Classify Command 1. How many inventory items with a market value of $25,000 or more are included in location 02? There are 4 inventory items with a market value of $25,000 or more that are included in location 02. 2. Use the drill-down feature to determine inventory items at cost (field = Inventory_Value_at_Cost) in Location 03 with a zero or negative value. (Hint: return to Classify by using the Classify button above the table.) How many are included? There are 3 inventory items with a market value of zero or a negative value that are included in location 03. Summarize Command 1. How many records are in the table you just created? There are 37 records in the table created 2. What is the Location/Product Class with the lowest inventory value at cost? Location 01 and Product Class 02 has the lowest inventory value at cost. Cross-tabulate Practice 1. How many managers are included in the Empmast Table? There are 8 managers that are included in the Empmast Table. 2. How many employees work in work department #D21? There are 7 employees who work in department #D21. 3. How many filters did you use to obtain the same information? I used 1 filter to obtain the same information. 4. Is the following statement true or false? Clicking on a row or column title in a command results screen creates a filter. This is True. 5. Compare your output for Cross-tabulate to the printout you made for Summarize in the last practice session. How is the information...

Words: 1015 - Pages: 5

Free Essay

Effects

...Scope and the Delimitation of the Study This study focused on the effects of the internet on the study habits of Bachelor of Secondary Education Major in Computer Education in Bulacan State University. Covered by this study were the 1st years to 4th year students of Bachelor in Secondary Education Major in Computer education in Bulacan State University main campus. The total populations of the student respondents from the 1st year to 4th year BSEd Major in Computer Education were twenty (20) students for year level with a total of eighty (80) respondents. Student’s classroom performance questionnaire of fifteen (15) items is categorized into process of learning and knowledge acquisition, construction of knowledge acquired and social interaction of students. The questionnaire are descriptive questionnaire which was used in gathering data and statistically treated using weighted mean and tabulated using frequency distribution table. The researcher utilized survey questionnaire and interviews in obtaining into requirements of the study. Population and Sample The respondents of the study were 1st year to 4t (School Year 2011-2012) the student respondents came from the College of Education in the main campus of Bulacan State University. Table 1 Distribution of the Student Respondents | Section | Major | No. of the Students/Respondents | Year | No. of the Student per Section | 1J | COMPUTER | 20 | 1ST | | 2J | COMPUTER | 20 | 2ND | | 3J | COMPUTER | 20...

Words: 318 - Pages: 2

Premium Essay

Boeing

...the current market for commercial airplanes was depressed because of terrorism risks, war, and SARS, a contagious illness that resulted in global travel warnings. Boeing’s board of directors would need to weigh those considerations before granting final approval to proceed with the project. The task for students is to evaluate the 7E7 project against a financial standard, the investors’ required returns. The case gives internal rates of return (IRR) for the 7E7 project under base-case and alternative forecasts. The students must estimate a weighted-average cost of capital (WACC) for Boeing’s commercial-aircraft business segment in order to evaluate the IRRs. As a result of that analysis, the students identify the key value drivers and distinguish, on a qualitative basis, the key gambles that Boeing is making. The general objective of this case is to exercise students’ skills in estimating a weighted-average cost of capital and cost of equity. The need for students to estimate a segment WACC draws out their abilities to critique different estimates of beta and to manipulate the levered-beta formulas. Boeing competes in both the commercial aircraft and the defense business. Thus, deriving the appropriate benchmark WACC for the 7E7 project requires isolating the commercial aircraft component from Boeing’s overall corporate WACC. In doing so, students...

Words: 7346 - Pages: 30

Premium Essay

Delta Plastics Inc

...Prepare a 3 –Sigma chart for both production processes using the new and standard material (use of quality report in “Delta Plastics, Inc, Case A.” chapter 5. See attached excel Charts for this answer. Discuss whether or not both processes are in control and what conclusion may be drawn. I tried to put the statistics together to have an overall perspective of the defects since most of them fall in the category of attributes rather than variables. I then took into consideration the 20 days as the period of observation rather than the four weeks. A P-chart methodology would rightly describe the products presented as good or bad because it is not a quick fix quality management system. After developing control limits with control P-charts to be able to understand the overall proportion of defects, I noticed curiously that both processes seem to be in control whereas from a first glance at the figures of the defects of the two materials, one has the impression that the new material is completely out of place for any serious business venture. Our problem was to determine whether there is a major shift in the process that is resulting in the alteration of that process. When we consider individual items, as for example, the cracks or the air bubbles, the process appears not to be in control. These particular defects virtually double with production from the new material. This is the source of the trauma that Jose is now experiencing. In the final analysis, we can conclude that...

Words: 862 - Pages: 4

Free Essay

Unit 6

...MAP4C Class #: _____ Date: ______________ Mean, Median, and Mode for Grouped Data Part A – Frequency Tables The following table shows the annual salaries earned by employees of a small company: Annual salary ($) 35 500 42 750 51 000 99 000 150 000 Totals Frequency 3 5 5 1 1 15 106 500 213 750 255 000 99 000 150 000 824 250 a) What is the mean salary? To find the mean of data in a frequency table: for each row… - multiply each value by its frequency - add up these values - divide by the frequency total 3(106500) + 5(213750) + 5(255000) +1(99000) +1(150000) 15 824250 = 15 = 54950 b) What is the median salary? There are 15 employees. ∴ the salary of the 8th employee is the median. The median salary is $42750 (count down from the top of the frequency table). c) What is the mode salary? There are two mode salaries. They are $42 750 and $51 000 (both with a frequency of 5). Page 1 of 4 MAP4C Class #: _____ Date: ______________ Part B – Grouped Data If data is already grouped into intervals, only an approximation of the centre of the data can be made. For grouped data, we use the midpoint of each interval. The following table shows the number of hours per day of watching TV in a sample of 500 people: Hours Frequency 0-1 55 2-3 87 4-5 145 6-7 90 8-9 73 10-11 35 12-13 15 a) What is the mean number of TV viewing hours in this group? b) What length of time is most often spent...

Words: 721 - Pages: 3