Question

Consider these two histograms representing two sets of data with 10 observations each. Which of the following is true?

A. The means are equal and the standard deviation of Plot 1 is smaller than the standard deviation of Plot 2.
B. The means are equal and the standard deviations are equal.
C. The mean and standard deviation of Plot 2 are larger than the mean and standard deviation of Plot 1.
D. The means are equal and the standard deviation of Plot 1 is larger than the standard deviation of Plot 2.

Answer 1

b. the means are equal and the standard deviations are equal.

Answer 2

The answer is D . The means are equal and the standard deviation of Plot 1 is larger than the standard deviation of Plot 2.

Explanation:

The histogram gives you information about the number of times a specific number appears on your sample. Then you can construct your sample looking at each histogram. For example in Plot 1 the value -2 appears two times. If you this, you obtain the following samples:

Plot 1: -2, -2, -1, -1, 0, 0, 1, 1, 2, 2

Plot 2: -2, -1, -1, 0, 0, 0, 0, 1, 1, 2

If you calculate the means by adding and dividing by the number of obs you find equal means (0) because the data is centered around 0. ( no deviations to left or right).

Now the standard deviation (sd) can be infered in the histogram. The sd measures the distance around the mean of the data. When data is concentrated very close to the mean, the sd is lower as in Plot 2 (More points are 0 or around zero in Plot 2). In plot 1 your points are farther apart from the mean of zero so the sd is higher.