Here are the ages of different cats at the shelter: 1, 7, 1, 1, 2, 2, 3, 1, 5, 7
1 How many cats are represented in this sample?
The distribution of these ages is shown in the histogram below:
2 Describe the shape of this histogram.
3 What is the mean age of the cats in this dataset?
4 How many cats are 1 year old? 2 years old? Fill in the table below. The first column has been done for you.
age |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
count |
4 |
5 Draw a star to locate the mean on the x-axis of the histogram above.
6 For each cat in the histogram above, draw a horizontal arrow under the axis from your star to the cat’s interval, and label the arrow with its distance from the mean. (For example, if the mean is 3 and a cat is in the 1yr interval, your arrow would stretch from 1 to 3, and be labeled with the distance "2")
To compute the standard deviation we square each distance and take the average, then take the square root of the average.
7 We’ve recorded the ages (N=10) shown in the histogram above in the table below, and listed the distance-from-mean for the four 1-year-old cats for you. As you can see, 1 year-olds are 2 years away from the mean, so their squared distance is 4. Complete the table.
age of cat |
1 |
1 |
1 |
1 |
2 |
2 |
3 |
5 |
7 |
7 |
distance from mean |
2 |
2 |
2 |
2 |
||||||
squared distance |
4 |
4 |
4 |
4 |
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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