In her art class, Ms. Walter has 12 students whose ages are listed below:
19, 20, 20, 20, 21, 22, 24, 24, 25, 25, 56, 60
She calculated the mean and the median of their ages. What is the relationship between these two values?
What mean and median did you find?
The mean is 28 and the median is 23???
Why do you think the mean is higher than the median?
336/12 = 28 right?
Right.
Note that all but two students are between 19 and 25. The other students are much older. That skews the mean, but doesn't affect the median.
The answer in the book says the mean is 8 years less than the median. Please explain.
By your and my calculations, there is 5 years between the median and the mean.
Thank you! I said the mean is 5 years more than the median.
To determine the relationship between the mean and the median, we first need to understand what these values represent.
The mean is also known as the average and is found by summing up all the values in a data set and dividing it by the total number of values. It gives us an idea of the typical or central value of the data set.
The median, on the other hand, is the middle value in a data set when it is arranged in ascending or descending order. If there is an even number of values, the median is calculated by taking the average of the two middle numbers. The median represents the "middle" value and is not affected by outliers in the data set.
Let's calculate the mean and the median for the given ages:
Step 1: Arrange the ages in ascending order:
19, 20, 20, 20, 21, 22, 24, 24, 25, 25, 56, 60
Step 2: Find the median:
Since there are 12 values, the median will be the average of the 6th and 7th numbers (21 and 22). Therefore, the median is 21.5.
Step 3: Find the mean:
To find the mean, sum up all the ages and divide it by the total number of ages.
Total = 19 + 20 + 20 + 20 + 21 + 22 + 24 + 24 + 25 + 25 + 56 + 60 = 336
Mean = 336 / 12 = 28
Now, let's analyze the relationship between the mean and the median:
In this case, the mean is 28 and the median is 21.5.
From this, we can conclude that the mean is greater than the median. This suggests that the data set is positively skewed, meaning that there are some higher values that are pulling the mean upwards.