#2 Find the mean of the data summarized in the given frequency distribution. Com
ID: 3045544 • Letter: #
Question
#2
Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 51.1 degrees. Low Temperature o Frequency 40-44 45-49 50-54 55-59 60-64 degrees. The mean of the frequency distribution is Round to the nearest tenth as needed.) Which of the following best describes the relationship between the computed mean and the actual mean? A. B. O c. ( D. The computed mean is close to the actual mean because the difference between the means is more than 5%. The computed mean is close to the actual mean because the difference between the means is less than 5%. The computed mean is not close to the actual mean because the difference between the means is less than 5% The computed mean is not close to the actual mean because the difference between the means is more than 5%.Explanation / Answer
Solution:
Here, we have to find mean for frequency distribution.
Mean = XF / F
Where, X is midpoint of the class and F is the frequency of class.
Calculations are given as below:
Midpoint X
F
X*F
42
3
126
47
7
329
52
12
624
57
5
285
62
1
62
Total
28
1426
Mean = XF / F
Mean = 1426/28 = 50.92857
Mean = 50.9
The mean of the frequency distribution is 50.9 degrees.
Which of the following best describes the relationship between the computed mean and the actual mean?
Answer: B. The computed mean is close to the actual mean because the difference between the means is less than 5%.
Question 2
Here, we have to compute range, variance, and standard deviation for the sample data.
Range = Maximum – minimum
Variance = (X - mean)^2/(n – 1)
SD = sqrt(Variance)
Table for calculations is given as below:
No.
X
(X - mean)
(X - mean)^2
1
148
7.5
56.25
2
147
6.5
42.25
3
148
7.5
56.25
4
140
-0.5
0.25
5
136
-4.5
20.25
6
124
-16.5
272.25
Total
843
0
447.5
Mean
140.5
Maximum
148
Minimum
124
Range
24
Variance
89.5
SD
9.460443964
Range = 148 – 124 = 24 mmHg
Sample variance = 447.5/(6 - 1) = 447.5/5 = 89.5 mmHg^2
Sample standard deviation = sqrt(89.5) = 9.5 mmHg
What should be the value of the standard deviation?
Answer: D. There is no way to tell what the standard deviation should be.
Midpoint X
F
X*F
42
3
126
47
7
329
52
12
624
57
5
285
62
1
62
Total
28
1426
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