Find the standard deviation, s, of sample data summarized in the frequency distr
ID: 3131410 • Letter: F
Question
Find the standard deviation, s, of sample data summarized in the frequency distribution table below by using the formula below, where x represents the class midpoint, f represents the class frequency, and n represents the total number of sample values. Also, compare the computed standard deviation to the standard deviation obtained from the original list of data values,11.1
(f•x2)(f•x)2n(n1)
Interval
20-26
27-33
34-40
41-47
48-54
55-61
62-68
Frequency
2
4
5
3
16
32
38
QUESTION: Find Standard deviation ?
(Round to one decimal place as needed.)
Consider a difference of 20% between two values of a standard deviation to be significant. How does this computed value compare with the given standard deviation,11.1?
A.
The computed value is significantly less than the given value.
B.
The computed value is not significantly different from the given value.
C.
The computed value is significantly greater than the given value.
Interval
20-26
27-33
34-40
41-47
48-54
55-61
62-68
Frequency
2
4
5
3
16
32
38
Explanation / Answer
We consider the midpoints to be the x values.
Consider:
Thus,
Variance = [Sum(x^2f) - Sum(xf)^2/Sum(f)]/[Sum(f)-1] = 108.270202
Hence,
Standard deviation = sqrt(Variance) = 10.40529683 [ANSWER]
*************************
As 20% of 11.1 is 0.20*11.1 = 2.22, and the difference is less than 2.22, then it is close. Hence,
OPTION B. B. The computed value is not significantly different from the given value. [ANSWER]
x f x f x^2 f 23 2 46 1058 30 4 120 3600 37 5 185 6845 44 3 132 5808 51 16 816 41616 58 32 1856 107648 65 38 2470 160550Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.