The sample mean x is the mathematical average for the given sample. The population mean μ is the mean value that can be determined for a specific characteristic of a population.
about 51 028.6
Practice makes perfect
We want to find the population mean μ of the given sample. To estimate the unknown population mean, we can find the sample mean x. The sample mean of the data set is the sum of the values divided by the total number of values in the set.
x=∑_()x_()/n
Now, we can consider the data in the given table.
Income of U.S. Households
14 300
52 100
74 800
51 000
91 500
72 800
50 500
15 000
37 600
22 100
40 000
65 400
50 000
81 100
99 800
43 300
32 500
76 300
83 400
24 600
30 800
62 100
32 800
21 900
64 400
73 100
20 000
49 700
71 000
45 900
53 200
45 500
55 300
19 100
63 100
Let's start by calculating the sum of the values in each column of the table.
Income of U.S. Households
14 300
52 100
74 800
51 000
91 500
72 800
50 500
15 000
37 600
22 100
40 000
65 400
50 000
81 100
99 800
43 300
32 500
76 300
83 400
24 600
30 800
62 100
32 800
21 900
64 400
73 100
20 000
49 700
71 000
45 900
53 200
45 500
55 300
19 100
63 100
Totals
327 500
328 100
353 900
365 100
411 400
Now, we can add the totals we calculated for all columns of the table.
327 500+ 328 100+ 353 900+
365 100+ 411 400
= 1 786 000
Finally, we know that the sum of the values is equal to 1 786 000 and that there are 35 values in our set. Let's substitute these values in the formula for the sample mean!
