Question

The Smiths recently had a family reunion. At this reunion the talk centered on some of the grandchildren and the spread in their ages. It was decided to develop a few statistics about the ages. Below are the ages of 20 randomly selected grandchildren.

4 4 4 5 6 7 8 9 9 10
10 12 15 18 19 21 22 25 27 30
Find the standard deviation

Answer 1

The standard deviation of the ages of the 20 randomly selected grandchildren is 10.12.

Step-by-step explanation:

The standard deviation measures the spread of data values around the mean. To calculate the standard deviation, you can follow these steps:

1. Find the mean of the data set by adding all the values together and dividing by the total number of values.
2. Subtract the mean from each individual data value.
3. Square each of the differences obtained in step 2.
4. Calculate the average of the squared differences by adding them together and dividing by the total number of values.
5. Take the square root of the average to get the standard deviation.

For the given ages of the 20 grandchildren:

Mean age = (4 + 4 + 4 + 5 + 6 + 7 + 8 + 9 + 9 + 10 + 10 + 12 + 15 + 18 + 19 + 21 + 22 + 25 + 27 + 30) / 20 = 10.53

Differences from the mean: (-6.53, -6.53, -6.53, -5.53, -4.53, -3.53, -2.53, -1.53, -1.53, -0.53, -0.53, 1.47, 4.47, 7.47, 8.47, 10.47, 11.47, 14.47, 16.47, 19.47)

Squared differences: (42.85, 42.85, 42.85, 30.62, 20.60, 12.43, 6.37, 2.35, 2.35, 0.28, 0.28, 2.15, 19.99, 55.93, 71.23, 110.33, 131.58, 210.94, 270.81, 378.52)

Average of squared differences = (42.85 + 42.85 + 42.85 + 30.62 + 20.60 + 12.43 + 6.37 + 2.35 + 2.35 + 0.28 + 0.28 + 2.15 + 19.99 + 55.93 + 71.23 + 110.33 + 131.58 + 210.94 + 270.81 + 378.52) / 20 = 102.46

Standard deviation = √102.46 = 10.12, rounded to two decimal places.