Describe the dataset. Which histogram is symmetrical?(1 point)

Question

Responses

A histogram shows the horizontal axis ranging from 12 to 22 in increments of 2 and the vertical axis ranging from 0 to 5 in increments of 1. The frequency plotted is as follows: 3 at range 12 to 14; 5 at range 14 to 16; 2 at range 16 to 18; 2 at range 18 to 20; 2 at range 20 to 22.
Image with alt text: A histogram shows the horizontal axis ranging from 12 to 22 in increments of 2 and the vertical axis ranging from 0 to 5 in increments of 1. The frequency plotted is as follows: 3 at range 12 to 14; 5 at range 14 to 16; 2 at range 16 to 18; 2 at range 18 to 20; 2 at range 20 to 22.

A histogram shows the horizontal axis ranging from 12 to 22 in increments of 2 and the vertical axis ranging from 0 to 5 in increments of 1. The frequency plotted is as follows: 1 at range 12 to 14; 2 at range 14 to 16; 3 at range 16 to 18; 2 at range 18 to 20; 1 at range 20 to 22.
Image with alt text: A histogram shows the horizontal axis ranging from 12 to 22 in increments of 2 and the vertical axis ranging from 0 to 5 in increments of 1. The frequency plotted is as follows: 1 at range 12 to 14; 2 at range 14 to 16; 3 at range 16 to 18; 2 at range 18 to 20; 1 at range 20 to 22.

A histogram shows the horizontal axis ranging from 12 to 22 in increments of 2 and the vertical axis ranging from 0 to 5 in increments of 1. The frequency plotted is as follows: 1 at range 12 to 14; 2 at range 14 to 16; 3 at range 16 to 18; 3 at range 18 to 20; 5 at range 20 to 22.
Image with alt text: A histogram shows the horizontal axis ranging from 12 to 22 in increments of 2 and the vertical axis ranging from 0 to 5 in increments of 1. The frequency plotted is as follows: 1 at range 12 to 14; 2 at range 14 to 16; 3 at range 16 to 18; 3 at range 18 to 20; 5 at range 20 to 22.

A histogram shows the horizontal axis ranging from 12 to 22 in increments of 2 and the vertical axis ranging from 0 to 5 in increments of 1. The frequency plotted is as follows: 4 at range 12 to 14; 5 at range 14 to 16; 5 at range 16 to 18; 1 at range 18 to 20; 2 at range 20 to 22.

Answer 1

To determine which histogram is symmetrical, we should look for a distribution where the frequencies mirror on either side of the center. Let’s evaluate each histogram based on the frequency data provided:

1. First Histogram:

   • Frequencies: 3, 5, 2, 2, 2
   • This distribution is not symmetrical as it is higher at the center (14-16) and decreases on both sides.

2. Second Histogram:

   • Frequencies: 1, 2, 3, 2, 1
   • This distribution is symmetrical. The frequencies mirror around 3 (at range 16-18) with 1 on either side (12-14 and 20-22) and 2 on either side (14-16 and 18-20).

3. Third Histogram:

   • Frequencies: 1, 2, 3, 3, 5
   • This distribution is not symmetrical as the right side (20-22) has a higher frequency compared to the left side.

4. Fourth Histogram:

   • Frequencies: 4, 5, 5, 1, 2
   • This distribution is not symmetrical, as the frequencies do not mirror around the center.

Based on this analysis, the second histogram is the only one that is symmetrical.