[Ezra Halleck]

The following data give the annual earnings (in thousands of dollars) of 20 low to moderate income families.
32.5 29.7 49.0 17.4 31.7 67.9 27.4
43.7 53.4 59.5 37.0 22.7 15.8 43.2
19.5 24.0 44.5 62.7 47.5 54.7
a. Order the data and create a table with columns x and x^2. Find their sums
b. Find the mean and median incomes (include units) and use them to comment on any skewing of this data.
c. Use the table to find the sample variance and standard deviation. Write the latter using units.

[Ezra Halleck]

posted by Tamisha Prou
x x2

15.8 249.64
17.4 302.76
19.5 380.25
22.7 515.29
24.0 576
27.4 750.76
29.7 882.09
31.7 1004.89
32.5 1056.25
37.0 1369
43.2 1866.24
43.7 1909.69
44.5 1980..25
47.5 2256.25
49.0 2401
53.4 2851.56
54.7 2992.09
59.5 3540.25
62.7 3931.29
67.9 4610.41
_____ _______

703.1 35425.9

mean 35.1
median 40.1

nEx2-E(x)2
___________
n(n-1)

20.35425.9- 703.1(2)
__________________
20(20-1)

708518-494349.61
________________
380

214168.39
__________
380

=563.6 sample variance
=24.0 standard deviation

[Ezra Halleck]

Looks good Tamisha. Just remember the units which are in thousands of dollars.

[Leonardo Calegare]

The formula for the sample variance is incorrect. The top part reads nEx2-Ex(2) and it should read nEx2-(Ex)^2.