Here are ten different family incomes: $43k, $62k, $39k, $141k, $58k, $82k, $41k, $73k, $68k, $73k
1 Draw the distribution of these incomes by placing a dot on the number line below. If two families have the same income, put one dot on top of the other. Finally, draw a box plot on the number line, making sure to label the axis and show each quartile.
2 Describe the shape of this box-plot.
3 What is the mean income of the families in this dataset?
4 How many families earn $39k? $43k? Fill in the table below. The first column has been done for you.
income |
$39k |
$41k |
$43k |
$58k |
$62k |
$68k |
$73k |
$82k |
$141k |
count |
1 |
5 Draw a star to locate the mean on the number line above.
6 For each family on the number line you drew,
-
Draw a horizontal arrow under the axis from the star you drew in #5 to the dot for that family’s income
-
Label the arrow with its distance from the mean.
e.g. if the mean is $50k and a family’s income is $82k, your arrow would stretch from $50k to $82k, and be labeled with the distance "$32k"
To compute the standard deviation we square each distance and take the average, then take the square root of the average.
7 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 to complete the table.
income (in 10s of thousands) |
39 |
41 |
43 |
58 |
62 |
68 |
73 |
73 |
82 |
141 |
distance from mean |
||||||||||
squared distance |
8 Add all the squared distances. What is their sum?
9 There are N=10 distances. What is N-1? Divide the sum by N-1. What do you get?
10 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, 1738598, 2031479, and 1501927). 
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