Other Descriptive Measures

CHAPTER 4 OTHER DESCRIPTIVE MEASURES

1.(a) 7, found by 10 – 3
(b) 6, found by =
(c) 2.4, found by =
(d) The difference between the highest number sold (10) and the smallest number sold (3) is 7. On average the number of service reps on duty deviates by 2.4 from the mean of 6.

3.(a) 51.32, found by (29.56-(-21.76))
(b) 7.07, found by=
(c) 11.20, found by = (168/15)
(d) The difference of 29.56 and –21.76 is 51.32. On average, one-year returns on common equity deviate 11.2 percent from the mean of 7.1 percent.

5.(a) 6.7 found by ($41.35-34.65).
(b) 38.4, found by=
(c) 1.51, found by ($21.11/14)
(d) The difference of 41.35 and 34.65 is 6.7. On average, the weekly share prices deviate $1.51 from the mean share price of $38.4.

7.(a) 56 928, found by = (284 640/5)
(b)S = 15393.35, found by

9.(a) $2.77, found by
(b) Variance = 1.26, found by

11.Range = 7.3, found by 11.6 – 4.3
Arithmetic mean = 6.94, found by= 34.7/5
Variance = 6.59, found by s2 ==32.972/5
Standard Deviation = 2.57

13.(a) Variance = 5.5
(b) , Variance = 5.5
(c) s = 2.35, found by

15.(a) Variance = 208.89, found by S2 =
(b) Variance = 208.89, found by
(c) Standard deviation = 14.45 found by

17.(a) , Variance = 4.67 found by
(b) Variance = 4.67
(c) s = 2.16, found by

19.(a) 25, found by 25 – 0
(b) 5.33 found by
(c) 28.42 found by

21.(a) $821 millions, found by ($975 millions – 154 millions)

(b) $209.42 millions, found by

23.69.1%, found by

25.(a) 95%

(b) 47.5%, 2.5%

27.78.52 %, found by (12.17/15.50)(100)

29.(a) There are two different measurements of the performance of the stocks.

(b) Mean (P/E) =16.06, found by (209/13), Standard deviation = 8.32, found by

CV(PE) =51.80 %, found by (8.30/16.08)(100)

Mean (returns) 21.41, found by (278/13), standard deviation =7.96, found by

37.17%, found by (7.96/21.41)(100)

31.(a) Mean =11.58, found by (173.65/15), the median is 10.23, and the standard deviation is 5.45, found by:

(b) CSP= 0.74, found by

(d) Skewed to the right. The value of the mean is greater than the value of median.

33.(a) Mean is 21.93, found by 328.9 / 15. Median is 15.8 and the standard deviation is 21.18, found as .

(b) CSP=0.87, found by .

35.Median = $20 041 millions, found by (14+1) =7.5 value from the lowest value of the ordered data set.. Half of the ordered market capitalization values are above it and the other half below it.

, found by (14+1)= 3.75 values from the lowest.

At most one quarter of the ordered market capitalization values are below it and at most three quarter of the ordered market capitalization values are above it.

, found by (14+1) = 11.25 value from the lowest.

At most three quarter of the ordered market capitalization values are below it and at most one quarter of the values are above it.

37.(a) Q1 = 33.25(L25=7.75)Q3 = 50.25 (L75=23.25)

(b) D2 = 27.8(L20=6.2)D8 = 52.6 (L80=24.8)

39.(a) Median =300,Q1 = 175Q3 = 875

(b)IQR==700, found by (875-175)

(d) Positive

41.

The distribution is positively skewed. The solid line (starting from the box) to the right of the box is longer than the line to the left of the box.

43.Line 1 and Line 3

45.103.2 to 104.8, found by 1042(0.4)

47.103.9, 104.1, found by 104.00.1)

49.3.7, found by

51.9, found by (3)2

Negatively skewed. The mean is smaller than the median. The longer tail is to the left. There are very few employees at the lower part of the age range with the highest concentration from the median to the upper part of the ages.

55.(a) 55, found by 72 – 17

(b) 43.2, found by = 432/10

57.(a) Population.

(b) , Population standard deviation = 185.4 thousands, found by

 = 185.4 thousands, found by

On average, the number of volumes held in libraries deviates from the mean by 185.4 thousands.

It allows a comparison if two groups have different scales/means.

59.(a) 40 km, found by (40-0)

The difference between the highest and the lowest distance travelled by employees is 40 km.

(b) 10.01 km, found by

61.(a)

(b)Skewed

(d)IQR = 10..7 (15.77 –5.07) (Minitab software)

It measures the variation of the middle 50% of the observations.

63(a) The median is approximately  750 000, Q1 600 000, and Q3 $950 000.

(b) Yes; more extreme points on the right.

65.(a) 38.06 to 93.53, found by 65.79  1.5(18.49)

(b) 28.10 percent, found by

67.(a) Mean = 17.16 Median = 16.35

(b) Standard deviation = 10.58, found by

(d) -4.0, 38.3, found by 17.16 2(10.58)
(e) CV = 61.66 %, found by %

(f) sk = 0.23, found by

(g)

(h) The distribution is nearly symmetrical. The mean is 17.16, the median is 16.35 and the standard deviation is 10.58. At most 75 percent of the companies have a value less than 27.4 and at most 25 percent have a value less than 7.825.

69.(a) Mean = $72.12, found by ($1009.71/14), Median = $71.40, and standard deviation = 21.67, found by

(b) 45th percentile = $64.76, found by $56.67+0.75(67.45-56.67).

80th percentile = $95.9, 12th value from the lowest value of the ordered data set.

(d)The data distribution is almost symmetrical. At most 25% of the data are below 7.83 and at most 75% of the data are above it.

71.(a)

Mean =19086323 (Minitab)

Median = 18209000(Minitab)

Q1 = 15267000 (Minitab)

Q3 = 22377000 (Minitab)

(b)0.41, found by

Yes

73.(a)See below. No. Median is not at the centre.

(b) The standard deviation of life expectancy for women is 11.10 years and for men is 9.62 years. Therefore, there is more variation in the life expectancy distribution for women than men.

75.Answer will depend on the latest data on Web site.

77.Answer will depend on the latest data on the Web site.

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