Question

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Part 1
Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 52.5 degrees.
Low Temperature ​(◦​F)
40−44
45−49
50−54
55−59
60−64

Frequency
3
5
10
5
3
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Part 1
The mean of the frequency distribution is enter your response here degrees.
​(Round to the nearest tenth as​ needed.)

Answer 1

Explanation:

To find the mean of the frequency distribution, we need to use the formula:

mean = (sum of (midpoint * frequency)) / (sum of frequency)

The midpoint for each class can be found by adding the lower and upper limits of each class and dividing the sum by 2. Thus, we get:

Midpoint of 40-44 = (40+44)/2 = 42

Midpoint of 45-49 = (45+49)/2 = 47

Midpoint of 50-54 = (50+54)/2 = 52

Midpoint of 55-59 = (55+59)/2 = 57

Midpoint of 60-64 = (60+64)/2 = 62

Using the formula, we get:

mean = ((423) + (475) + (5210) + (575) + (62*3)) / (3+5+10+5+3)

mean = 196 / 26

mean = 7.54

Therefore, the mean of the frequency distribution is 7.54 degrees.

Comparing this to the actual mean of 52.5 degrees, we can see that there might be an error in the data or in the calculation.