The data below are the ages of six cousins, in vears. Find the following descrip

Question

The data below are the ages of six cousins, in vears. Find the following descriptive statistics Include units with your answers a. Mean b. Median c. Mode d. Range e. Variance (use the formula for a sample) f. Standard Deviation (use the formula for a sample) 1. 12 2. Two years have passed, and all six cousins are now 2 years older. Add 2 to each number and compute the mean and standard deviation (for a sample) of the resulting data. Describe how adding 2 to each data value affected the mean and the standard deviation. a. b.

Explanation / Answer

1. The ages are 12, 11, 1, 9, 7, 8

a. Mean = (12 + 11 + 1 + 9 + 7 + 8) / 6

= 8.

b. Sorted list is 1, 7, 8, 9, 11, 12

Median = (8 + 9) / 2

= 8.5

c. Mode is the most repeating value

In this case all six values are the mode

12, 11, 1, 9, 7, 8.

d. Range is (1-12).

e. Sum of the squares of differences SS = (12-8)2 + (11-8)2 + (1-8)2 + (9-8)2 + (7-8)2 + (8-8)2

= 42 + 32 + (-7)2 + 12 + (-1)2 + 02

= 16 + 9 + 49 + 1 + 1 + 0

= 76

Variance s2 = SS / (N-1)

= 176 / 5

= 15.2

f. Standard deviation s = 15.2 = 3.8987

2. a. The new ages are

14, 13, 3, 11, 9, 10

a. Mean = (14 + 13 + 3 + 11 + 9 + 10) / 6

= 10.

Sum of squares of differences = (14-10)2 + (13-10)2 + (3-10)2 + (11-10)2 + (9-10)2 + (10-10)2

= 42 + 32 + (-7)2 + 12 + (-1)2 + 02

= 16 + 9 + 49 + 1 + 1 + 0

= 76

Variance s2 = SS / (N-1)

= 176 / 5

= 15.2

Standard deviation s = 15.2 = 3.8987

b. We see that adding 2 to each data adds 2 to the mean. The standard deviation does not change at all.

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