Find the standard deviation, s, of sample data summarized in the frequency distribution table given below by using the formula below, where x represents the class midpoint, f represents the class frequency, and n represents thetotal number of sample values. Also, compare the computed standard deviation to the standard deviation obtained from the original list of data values, 9.0.n(n - 1)Interval30-3940-4950-5960-6970-7980-892241152Frequency1.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, 9.0?O A. The computed value is significantly greater than the given value.O B. The computed value is significantly less than the given value.OC. The computed value is not significantly different from the given value.Click to select your answer(s).O vi 8:45DELL%23$678.4.2ur

Answered: PDUPIS aU Du Deviation, S, Of Sample…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Find the standard deviation, s, of sample data summarized in the frequency distribution table given 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, 9.0.
n(n - 1)
Interval
30-39
40-49
50-59
60-69
70-79
80-89
22
41
15
2
Frequency
1.
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, 9.0?
O A. The computed value is significantly greater than the given value.
O B. The computed value is significantly less than the given value.
OC. The computed value is not significantly different from the given value.
Click to select your answer(s).
O vi 8:45
DELL
%23
$
6
7
8.
4.
2
u
r

Expert Solution

Step 1

Given data is used to fit a standard deviation for the following data. the data is in inclusive so we need to covert into exclusive by adding 0.5 to the upper limit. and subtracting 0.5 to the lower limit.

Step 2

class interval	friquencies(fi)	mid values (mi)	fi*mi	${(m i - x b a r)}^{2}$	$f i {(m i - x b a r)}^{2}$
29.5-39.5	1	34.5	34.5	463.9716	463.9716
39.5-49.5	22	44.5	979	133.1716	2929.7752
49.5-59.5	41	55.5	2275.5	0.1936	7.9376
59.5-69.5	15	65.5	982.5	89.4916	1342.374
69.5-79.5	5	75.5	377.5	378.6916	1893.458
79.5-89.5	2	85.5	171	867.8916	1735.7832

Total =86 =4820 =8373.2996

Step 3

Mean = $({\sum f i m i}_{i = 1}^{n}) \div N$ =4820/86 = 56.04

Variance = $[f i {(x i - x b a r)}^{2}] \div N$ =8373.2996/86 = 97.3639

standard deviation = $\sqrt{v a r i a n c e}$ =9.86

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