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Estimate the mean of the distribution. You are given full credit if the estimate is within 2 units of the actual mean. It is okay to use decimals in your answer.

User Andzep
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1 Answer

6 votes

Answer:

about 4.5

Explanation:

You want the mean of the distribution shown in the given histogram.

Mean

The mean is the sum of data values, divided by their number. The histogram bars show the number of each of the data values. For this purpose, we take the data value to be the midpoint of the interval.

For example, the leftmost bar covers the interval from 0 to 1 and has a height of about 13. We are assuming it represents 13 data values of 0.5 each.

The heights of the bars from 0 to 25 are estimated to be ...

{13, 52, 49, 28, 28, 23, 14, 13, 10, 4, 2, 4, 2, 1, 1, 0, 2, 0, 0, 0, 1, 1, 1, 1, 1}

Multiplying these values by {0.5, 1.5, 2.5, ..., 24.5} and adding the products gives a total of all 251 data values of 1134.5. Their mean is ...

1134.5/251 ≈ 4.52

The mean of this distribution is about 4.5.

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Additional comment

The graph is difficult to read precisely in all cases. We suppose there might be a total of 250 data points, rather than 251, but it is not clear where we have read the graph incorrectly. This should not substantially affect the computed mean.

The mode is about 1.5, the median is about 3.5, and the right-skew tells us the mean will be higher than the median. So, an estimate of 4.5 seems about right.

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Estimate the mean of the distribution. You are given full credit if the estimate is-example-1
User Felix Cen
by
7.2k points