The histogram below shows the ages of ten cats at the shelter:

1 Describe the shape of this histogram.

2 How many cats are 1 year old? 2 years old? Fill in the table below by reading the histogram. The first column has been done for you.

age

1

2

3

4

5

6

7

count

4

3 What is the mean age of the cats in this histogram?

4 Draw a star to locate the mean on the x-axis of the histogram above.

5 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")

6 We want to summarize all 10 distances from the mean into a single number. What number do you think will best summarize those distances?

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 10 ages 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

8 Add all the squared distances. What is their sum?

9 What is the average squared distance?

10 Take the square root to find the standard deviation!

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