a. Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 53.3 degrees. Low Temperature ( ◦ F) 40 − 44 45 − 49 50 − 54 55 − 59 60 − 64 Frequency 1 4 11 6 2 The mean of the frequency distribution is degrees. (Round to the nearest tenth as needed.) b. Find the standard deviation of the data summarized in the given frequency distribution.

Step-by-step explanation:

Given

The sumarized data

Solving (a): The mean

First, we calculate the class mid-points (x); This is the mean of the class intervals.

For 40 - 44, x = (40 + 44)/2 = 42. This is applied to all other classes.

So:

x  42   47   52    57    62

f    1      4     11      6       2

The mean is:

Compared to the actual mean (53.3), the computed mean is lower

Solving (b): The standard deviation

This is calculated using:

So, we have:

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