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Use the image to answer the question.

A histogram is shown. From left to right, the horizontal axis has numbers from 2 to 38 in increments of 4. The vertical axis is labeled Frequency. From bottom to top, the vertical axis has numbers from 3 to 30 in increments of 3.

Which number is the best estimate of the standard deviation for the distribution shown?

(1 point)
Responses

16
16

8
8

4
4

20

1 answer

To estimate the standard deviation from a histogram, one would typically look at the spread of the data around the mean. However, since I cannot see the image or histogram you are referring to, I can give you guidance on how to estimate the standard deviation based on a histogram.

  1. Identify the mean: Look for the center of the distribution; this will give you a starting point for calculating spread.

  2. Assess the spread: Look at the width of the histogram bars. A wider spread indicates a larger standard deviation.

  3. Use empirical rules if applicable: For a normal distribution, about 68% of the data falls within one standard deviation of the mean. If your data looks approximately normal, you may use this as a reference for estimating the standard deviation.

Considering your answer choices, if the histogram shows a moderate spread, then 8 might be reasonable if the data is centered around a number significantly different from the limits seen. If the distribution is very wide, you might consider the max of 16 or 20.

If the data is tightly grouped, then possibly 4 suggests a narrow spread.

Unfortunately, without seeing the histogram or knowing the specific distribution shape, it’s difficult to give a definitive answer. Based on typical histograms, if you see a significant spread, I might choose 8 as a reasonable estimate. But please evaluate it against your histogram to make the best choice.