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Statistics Hw

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11 6l | 034 | | 6h | 667899 | | 7l | 00122244 | | 7h | | Stem=Tens | 8l | 001111122344 | Leaf=Ones | 8h | 5557899 | | 9l | 03 | | 9h | 58 | |

This display brings out the gap in the data: There are no scores in the high 70's.
13.
a. | | | | 12 | 2 | Leaf = ones | 12 | 445 | Stem = tens | | 12 | 6667777 | | | 12 | 889999 | | | 13 | 00011111111 | | | 13 | 2222222222333333333333333 | | | 13 | 44444444444444444455555555555555555555 | 13 | 6666666666667777777777 | | | 13 | 888888888888999999 | | | 14 | 0000001111 | | | 14 | 2333333 | | | 14 | 444 | | | 14 | 77 | | |

The observations are highly concentrated at 134 – 135, where the display suggests the typical value falls.

b.

The histogram is symmetric and unimodal, with the point of symmetry at approximately 135.
15
Crunchy | | Creamy | | 2 | 2 | 644 | 3 | 69 | 77220 | 4 | 145 | 6320 | 5 | 3666 | 222 | 6 | 258 | 55 | 7 | | 0 | 8 | |

Both sets of scores are reasonably spread out. There appear to be no outliers. The three highest scores are for the crunchy peanut butter, the three lowest for the creamy peanut butter.

17 a Number Nonconforming Frequency RelativeFrequency(Freq/60) 0 7 0.117 1 12 0.200 2 13 0.217 3 14 0.233 4 6 0.100 5 3 0.050 6 3 0.050 7 1 0.017 8 1 0.017 doesn't add exactly to 1 because relative frequencies have been rounded 1.001 b The number of batches with at most 5 nonconforming items is 7+12+13+14+6+3 = 55, which is a proportion of 55/60 = .917. The proportion of batches with (strictly) fewer than 5 nonconforming items is 52/60 = .867. Notice that these proportions could also have been computed by using the relative frequencies: e.g., proportion of batches with 5 or fewer nonconforming items = 1- (.05+.017+.017) = .916; proportion of batches with fewer than 5 nonconforming items = 1 - (.05+.05+.017+.017) = .866.

c. The following is a Minitab histogram of this data. The center of the histogram is somewhere around 2 or 3 and it shows that there is some positive skewness in the data. Using the rule of thumb in Exercise 1, the histogram also shows that there is a lot of spread/variation in this data.

19. a. From this frequency distribution, the proportion of wafers that contained at least one particle is (100-1)/100 = .99, or 99%. Note that it is much easier to subtract 1 (which is the number of wafers that contain 0 particles) from 100 than it would be to add all the frequencies for 1, 2, 3,… particles. In a similar fashion, the proportion containing at least 5 particles is (100 - 1-2-3-12-11)/100 = 71/100 = .71, or, 71%.

b. The proportion containing between 5 and 10 particles is (15+18+10+12+4+5)/100 = 64/100 = .64, or 64%. The proportion that contain strictly between 5 and 10 (meaning strictly more than 5 and strictly less than 10) is (18+10+12+4)/100 = 44/100 = .44, or 44%.

c. The following histogram was constructed using Minitab. The data was entered using the same technique mentioned in the answer to exercise 8(a). The histogram is almost symmetric and unimodal; however, it has a few relative maxima (i.e., modes) and has a very slight positive skew.

21 a. A histogram of the y data appears below. From this histogram, the number of subdivisions having no cul-de-sacs (i.e., y = 0) is 17/47 = .362, or 36.2%. The proportion having at least one cul-de-sac (y 1) is (47-17)/47 = 30/47 = .638, or 63.8%. Note that subtracting the number of cul-de-sacs with y = 0 from the total, 47, is an easy way to find the number of subdivisions with y 1.

b. A histogram of the z data appears below. From this histogram, the number of subdivisions with at most 5 intersections (i.e., z 5) is 42/47 = .894, or 89.4%. The proportion having fewer than 5 intersections (z < 5) is 39/47 = .830, or 83.0%.

29. Complaint | Frequency | Relative Frequency | B | 7 | 0.1167 | C | 3 | 0.0500 | F | 9 | 0.1500 | J | 10 | 0.1667 | M | 4 | 0.0667 | N | 6 | 0.1000 | O | 21 | 0.3500 | | 60 | 1.0000 |

37 , , . The median or the trimmed mean would be good choices because of the outlier 21.9.

38 a. The reported values are (in increasing order) 110, 115, 120, 120, 125, 130, 130, 135, and 140. Thus the median of the reported values is 125.

b. 127.6 is reported as 130, so the median is now 130, a very substantial change. When there is rounding or grouping, the median can be highly sensitive to small change.

39

a. so ;

b. 1.394 can be decreased until it reaches 1.011(the largest of the 2 middle values) – i.e. by 1.394 – 1.011 = .383, If it is decreased by more than .383, the median will change.

45. a. = = 577.9/5 = 115.58. Deviations from the mean: 116.4 - 115.58 = .82, 115.9 - 115.58 = .32, 114.6 -115.58 = -.98, 115.2 - 115.58 = -.38, and 115.8-115.58 = .22. b. s2 = [(.82)2 + (.32)2 + (-.98)2 + (-.38)2 + (.22)2]/(5-1) = 1.928/4 =.482, so s = .694. c. = 66,795.61, so s2 = = [66,795.61 - (577.9)2 /5]/4 = 1.928/4 = .482. d. Subtracting 100 from all values gives , all deviations are the same as in part b, and the transformed variance is identical to that of part b.

57 a. 1.5(IQR) = 1.5(216.8-196.0) = 31.2 and 3(IQR) = 3(216.8-196.0) = 62.4. Mild outliers: observations below 196-31.2 = 164.6 or above 216.8+31.2 = 248. Extreme outliers: observations below 196-62.4 = 133.6 or above 216.8+62.4 = 279.2. Of the observations given, 125.8 is an extreme outlier and 250.2 is a mild outlier. b. A boxplot of this data appears below. There is a bit of positive skew to the data but, except for the two outliers identified in part (a), the variation in the data is relatively small.

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