Shown below are ten different family incomes:
$43k, $62k, $39k, $141k, $58k, $82k, $41k, $73k, $68, $73k
1 Draw a number line representing the distribution of this data.
2 What is the mean income of the families in this dataset?
3 Draw a star to locate the mean on the x-axis of the histogram above.
4 For each family on the number line you drew, draw a horizontal arrow under the axis from your star to that family’s interval, and label the arrow with its distance from the mean. (For example, if the mean is 50 and a family’s income is $82k, your arrow would stretch from 50 to 82, and be labeled with the distance "32")
To compute the standard deviation we square each distance and take the average, then take the square root of the average.
5 For each of the 10 incomes in the table below, list the distance-from-mean for each income, using the mean you computed above. Then fill in the squared distance in the next row.
income (in 10s of thousand) |
39 |
41 |
43 |
58 |
62 |
68 |
73 |
73 |
82 |
141 |
distance from mean |
||||||||||
squared distance |
6 Add all the squared distances. What is their sum?
7 What is the average squared distance?
8 Take the square root to find the standard deviation!
These materials were developed partly through support of the National Science Foundation,
(awards 1042210, 1535276, 1648684, and 1738598). 
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