The problem asks to determine the relationship between the mean and the median based on the given histogram. The options are: A. The mean will be less than the median. B. The mean will be greater than the median. C. The mean and the median will be about the same. D. There is no way to tell the relationship between the mean and the median.

1. Problem Description

The problem asks to determine the relationship between the mean and the median based on the given histogram. The options are:

A. The mean will be less than the median.

B. The mean will be greater than the median.

C. The mean and the median will be about the same.

D. There is no way to tell the relationship between the mean and the median.

2. Solution Steps

The histogram represents the frequency distribution of data. To determine the relationship between the mean and the median, we need to observe the shape of the distribution.

The histogram shows the following frequencies for each value:

12: 1

13: 1

14: 1

15: 1

16: 1

17: 2

18: 5

19: 1

20: 1

The total number of data points is $1+1+1+1+1+2+5+1+1 = 14$.

The median is the middle value. Since there are 14 data points, the median will be the average of the 7th and 8th values when the data is sorted.

The sorted data is: 12, 13, 14, 15, 16, 17, 17, 18, 18, 18, 18, 18, 19,

2

0. The 7th value is 17 and the 8th value is

1

8. So the median is $\frac{17+18}{2}=17.5$.

The mean is the average of all the values. The sum of all the values is:

$12+13+14+15+16+17*2+18*5+19+20 = 12+13+14+15+16+34+90+19+20 = 233$.

The mean is $\frac{233}{14} \approx 16.64$.

Since the mean (16.64) is less than the median (17.5), the correct statement is A.

3. Final Answer

A. The mean will be less than the median.