QUESTION 1
The level of measurement is the relationship among values that are assigned to the attributes for a variable. There are four levels of measurement. Knowing the different levels of measurement helps to decide how to interpret the data from variables as well as deciding the statistical analysis that is appropriate on the values that are assigned. These four levels are nominal, ordinal interval, and ration. The lowest level is nominal and the highest is ratio.
The most basic level of measurement is the nominal level. In nominal measurement the numerical values or responses are labels, categories or names. Some examples would be gender, religion, favorite color, etc. The key point about nominal measurement is that it does not imply any ordering among the responses. The responses are merely named uniquely.
Ordinal level of measurement is the next level. Data that is noted or recorded at this level is ranked or counted. The data is arranged in some type of order however the difference between the data values cannot be determined or are meaningless. The differences in two ordinal scales cannot be assumed, they are only ranked or rated on a relative scale. Ordinal scales are usually non-numeric thoughts like satisfaction, happiness or discomfort. You can determine central tendency on a set of ordinal data using mode or median.
Interval level of measurement is the next level and can be described as measurement based on a scale with a known unit of measurement. In interval measurement we are able to determine the order as well as the exact difference between the values. An example would be time because the increments are known, consistent and are measurable. The difference between interval values is meaningful, however, with interval measurement there is no “true zero.” Therefore, it is impossible to compute ratios with interval data, however the data has meaning.
The highest level of measurement is ration. Most quantitative variables such as height, weight and changes in stock prices are recorded at the ratio level of measurement. Ratio measurement tells us about the order as well as the exact value between units and has an absolute zero point. Ratio measurement is very useful when it comes to statistical analysis. Sums can be calculated (mean, median, mode) as well as ratios and a meaningful number will result.
There is an implied order in the level of measurement. At the lower levels such as nominal and ordinal, assumptions tend to be less restrictive. Measurement at the interval and ration level tend to be more desirable in statistical analysis because of the use of statistical procedures available for means and standard deviation.
Table 1. Summary of the Levels of Measurement SUMMARY FUNCTIONS | NOMINAL | ORIDNAL | INTERVAL | RATIO | | | | | | COUNTS - FREQUENCY DISTRIBUTION |  |  |  |  | MODE, MEDIAN | |  |  |  | "ORDER" OF VALUE IS KNOWN | |  |  |  | CAN QUANTIFY THE DIFFENCE BETWEEN EACH VALUE | | |  |  | CAN +/- VALUE | | |  |  | CAN ×/÷ VALUES | | | |  | HAS "TRUE ZERO" | | | |  |
QUESTION 2 The stem-and-leaf plot is a display that arranges data to show its shape and distribution. In a stem-and-leaf plot data value are split into a stem along the vertical axis and a leaf along the horizontal axis. The leaf usually represents the last digit of the number and the other digits to the left of the leaf form the stem. The number 789 would be split as 78 representing the stem and the 9 would represent the leaf. The stem-and-leaf display is most useful when data is not too numerous. Having a histogram over a stem-and-plot display helps to show the frequency or each interval as well as it displays al of the individual values within that interval. A boxplot is a graphical display that summarizes the median, upper and lower quartiles, the minimum and maximum data values in a data set. The boxplot can be used to show trends, patterns and forecasting for the future. For example, a repair shop may want to offer a coupon for oil changes. They know that they will more than likely get more customers and will need to possibly have more personnel on hand to handle the extra load. The owner will want to collect some information about oil changes such as the time it takes for an average oil change and how many fell within that time frame. A boxplot which is based on quartiles would give him a picture of what this looks like. MegaStat is an add-in tool that performs statistical analysis in Excel. One advantage of MegaStat is that is show if a variable contains outliers. Outliers are data values that are very different from the other data in your set and this can skew your results. An outlier causes the mean to have a higher or lower value biased in favor of the direction of the outlier. Outlier values fall outside of an overall trend that is present in the data. They are sometimes caused by error or possibly a previously unknown tendency. Outliers don’t fit the general trend of the data and are sometimes left out of the calculation of the mean to more accurately represent the value.