Questions: A grandfather wants to know the average height of all his grandchildren. He finds that the heights of his 9 grandchildren are given in inches by 63, 71, 60, 59, 74, 60, 60, 75, 58. What is the population mean of the height of his grandchildren in inches? Round your answer to the nearest tenth of an inch and do not include units.

A grandfather wants to know the average height of all his grandchildren. He finds that the heights of his 9 grandchildren are given in inches by 63, 71, 60, 59, 74, 60, 60, 75, 58. What is the population mean of the height of his grandchildren in inches? Round your answer to the nearest tenth of an inch and do not include units.

Transcript text: A grandfather wants to know the average height of all his grandchildren. He finds that the heights of his 9 grandchildren are given in inches by \[ 63,71,60,59,74,60,60,75,58 \] What is the population mean of the height of his grandchildren in inches? Round your answer to the nearest tenth of an inch and do not include units.

Solution

Solution Steps

Step 1: Sum all the data points

To find the population mean, we first sum all the data points in the set. This is represented mathematically as \(\sum_{i=1}^{N} x_i\), where \(x_i\) is each individual data point and \(N\) is the total number of data points. In this case, the total sum is \(\sum_{i=1}^{N} x_i = 580\).

Step 2: Calculate the mean

The mean (average) of the data set is calculated by dividing the total sum by the number of data points (\(N\)). The formula for the mean is \(\mu = \frac{\sum_{i=1}^{N} x_i}{N}\). Substituting the values, we get \(\mu = \frac{580}{9} = 64.444\).

Step 3: Round the result

If required, the result is rounded to the nearest specified decimal places. After rounding to 1 decimal places, the mean is 64.4.