Statistics Case

3.2

The following is a set of data from a sample of n = 6:

7 4 9 7 3 12

(a) Compute the mean, median, and mode

Mean = 7 7+4+9+7+3+12 = 42/6 = 7

Median = 7 42 / 6 = 7

Mode = 7 3 4 7 7 9 12

(b) Compute the range, variance, standard deviation, and coefficient of variation

12 - 3 = 9 ...range = 9

Variance = 10.8

7-7=0, 7-4=3, 7-9=-2, 7-7=0, 7-3=4, 7-12=-5

9 4 16 25 = 54 = 10.8

(n) 6 -1 = 5 5

Standard deviation = 10.8 = 3.286

Coefficient of variation = 3.286/7 * 100% = 46.948%

(c) Computer the Z scores. Are there any others?

0, -0.913, 0.609, 0, -1.217, 1.522 / No. There are no Z scores greater or smaller than 3.0 or -3.0

(d) Describe the shape of the data set

It is symmetrical because the mean and median are equal

3.13

The file 'ChocolateChip contains the cost (in cents) per 1-ounce serving for a sample of 13 chocolate chip cookies. The data is below:

54 22 25 23 36 43 7 43 25 47 24 45 44

(a) Compute the mean, median, and mode

Mean = 33.69 7, 22, 23, 24, 25, 25, 36, 43, 43, 44, 45, 47, 54 = 438

Median = 438 / 13 = 33.69

Mode = 36 7, 22, 23, 24, 25, 25, 36, 43, 43, 44, 45, 47, 54

(b) Compute the variance, standard deviation, range, coefficient of variation, and Z scores. Are there any outliers? Explain.

54 - 7 = 47 ...range = 47

Variance = 359.08

47- 7 = 40 + 47-22 = 25 + 47-23 = 24 + 47-24 = 23 + 47-25 = 22 + 47-25 = 22 + 47-36 = 11 + 47-43 = 4 + 47-43 = 4 + 47-44 = 3 + 47-45 = 2 + 47-47 = 0 + 47-54 = 7

Sq: 1600 + 625 + 576 + 325 + 484 + 484 + 121 = 4309 = 359.08

(n) 13-1 = 12

Standard deviation = 359.08 = 18.949

Coefficient of variation = 359.08/47 * 100% = 7.64%

(c) Are the data skewed? If so, how?

Yes. The mean and median are not equal

(d) Based on the results of (a) through (c), what conclusions can you reach concerning the cost of chocolate chip cookies?

Positive Skew - skewed to the right

3.34

Using the data in Mutual Funds.

(a) Construct a Pivot Table of the mean three-year return by category and risk

Average of 3-year return Risk

Category Average High Low Total

Large Cap 9.7 6.62519685 12.24026846 9.673333333

Mid Cap 13.27818182 10.74883721 15.54242424 12.45747126

Small Cap 14.83292683 10.58873239 15.07 12.38237705

Total 11.68617363 9.209577465 13.05990099 10.99297235

(b) Construct a Pivot Table of the standard deviation of the three-year return by category and risk.

StdDev of 3-Year Return Risk

Category Average High Low Total

Large Cap 3.00900383 3.722005956 2.497537151 3.774530753

Mid Cap 2.868325806 3.02956973 2.152764255 3.378703523

Small Cap 2.712979997 4.209177723 2.747458155 4.22195624

Total 3.700301011 4.233938556 2.820663976 4.065661636

(c) What conclusion can you reach concerning differences between the