Question
Asked Sep 3, 2019
285 views
Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of
51.951.9
degrees.
 
Low Temperature
​(circle◦​F)
40minus−44
45minus−49
50minus−54
55minus−59
60minus−64
 
Frequency
22
66
99
77
11
 
The mean of the frequency distribution is
nothing
degrees.
check_circle

Expert Answer

Step 1

Note:

Hi! Thank you for posting the question. However, in our display of the website, the actual mean is showing as “51.951.9”. We have considered it as 51.9 and proceeded with the problem. Also, the classes of Low Temperature are showing as “40minus–44”, “45minus–49”, etc. We have considered these as 40 – 44, 45 – 49, etc., as in “40 to 44”, “45 to 49”,… and solved the problem.

Step 2

Calculation:

In order to find the mean of a grouped frequency, the mid-point of each class is considered as the representative of that class.

If the mid-point of a class is taken as x and the frequency as f, then the mean is: (Σxf) / (Σf).

The following table shows the calculation of the mean:

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Image Transcriptionclose

Low Temperature (Classes)x 40 44 42 22 924 45-49 47 66 3102 5148 4389 50 54 55 59 52 99 57 77 60-64 62 11 682 Σf-275|Σf-14,245 Total

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Step 3

The mean and its comparison:

Thus, the mean of the grouped frequency distribution is:

mean = (Σxf) / (Σf)

= 14,245/275

= 51.8.

The actual mean is 51.9.

The mean of the grouped frequency distribution (51.8°F) and the actua...

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Statistics

Data

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