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: 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.
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: 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.

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.
Skip to navigation

Answer 1

To determine which histogram is symmetrical, we can analyze the provided frequency distributions. A symmetrical histogram will have frequencies that are mirrored around its center.

Here's the breakdown of each histogram's frequency distributions:

1. First Histogram:

   • 12 to 14: 1
   • 14 to 16: 2
   • 16 to 18: 3
   • 18 to 20: 3
   • 20 to 22: 5
   • Observation: This is not symmetrical; it increases until the range of 20 to 22, which has the highest frequency.

2. Second Histogram:

   • 12 to 14: 4
   • 14 to 16: 5
   • 16 to 18: 5
   • 18 to 20: 1
   • 20 to 22: 2
   • Observation: This is also not symmetrical; frequencies on the left are high and drop significantly after the mid-point.

3. Third Histogram:

   • 12 to 14: 3
   • 14 to 16: 5
   • 16 to 18: 2
   • 18 to 20: 2
   • 20 to 22: 2
   • Observation: This histogram is not symmetrical; the heights do not create a mirrored effect.

4. Fourth Histogram:

   • 12 to 14: 1
   • 14 to 16: 2
   • 16 to 18: 3
   • 18 to 20: 2
   • 20 to 22: 1
   • Observation: This histogram is symmetrical. The frequencies increase until the center (16 to 18) and then decrease, resembling a mirror image around the center of the range.

Conclusion: The fourth histogram is the only one that is symmetrical.