Question

For the histogram on the right determine whether the mean is greater​ than, less​ than, or approximately equal to the median. Justify your answer. 0 5 10 15 20 A histogram has a vertical axis labeled from 0 to 20 in increments of 5. Six adjacent vertical bars with equal width extend from the horizontal axis have heights, from left to right, as follows: 3, 4, 7, 10, 13, and 10. Which of the following is​ correct? A. x overbar equals Upper M because the histogram is symmetric. B. x overbar less than Upper M because the histogram is symmetric. C. x overbar greater than Upper M because the histogram is skewed left. D. x overbar less than Upper M because the histogram is skewed left. E. x overbar greater than Upper M because the histogram is skewed right. F. x overbar equals Upper M because the histogram is skewed right.

Answer 1

Answer:

Option D is correct.

x overbar less than Upper M because the histogram is skewed left.

Step-by-step explanation:

Note that x overbar represents the mean and upper M represents the median.

The median is the variable at the middle of the distribution of distribution when all the variables are arranged in ascending or descending order.

The total frequency for this distribution is 3+4+7+10+13+10 = 47

the median will be at the middle of this distribution; that is, at the 24th position.

The 24th position is on the 4th bar (the very end of the 4the bar).

The mean is the average of a distribution. It is the sum of variables in the distribution divided by the number of variables in the distribution.

For an histogram, the number in the middle of each bar is used to calculate the mean.

Let us assume that the width of each bar is 5 and the midpoint of the first bar is x, then the midpoint of the next bar will be x+5, the next bar will be x+10, etc.

Sum of the variables = (x)(3) + (x+5)(4) + (x+10)(7) + (x+15)(10) + (x+20)(13) + (x+25)(10) = 47x + 750

mean = (47x+750)/47

Mean = (x + 15.95)

This value indicates that the mean is on the 4th bar. But like we obtained, the median was at the end of the 4th bar, the mean is closer to the midpoint of the bar. (Recall that the midpoint of the bar is x+15).

This indicates that the mean is less than the median.

When the mean is less than the median, it means that less variables fall below the mean, more variables are found above the mean and it is a skewed left distribution.

Hope this Helps!!!