Question

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. sequalsStartRoot StartFraction n left bracket Summation from nothing to nothing left parenthesis f times x squared right parenthesis right bracket minus left bracket Summation from nothing to nothing left parenthesis f times x right parenthesis right bracket squared Over n left parenthesis n minus 1 right parenthesis EndFraction EndRoot Interval 20​-29 30​-39 40​-49 50​-59 60​-69 70​-79 Frequency 1 21 40 20 8 5 Standard deviationequals 11.0 ​(Round to one decimal place as​ needed.)

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,

9.09.0.

sequals=StartRoot StartFraction n left bracket Summation from nothing to nothing left parenthesis f times x squared right parenthesis right bracket minus left bracket Summation from nothing to nothing left parenthesis f times x right parenthesis right bracket squared Over n left parenthesis n minus 1 right parenthesis EndFraction EndRootn∑f•x2−∑(f•x)2n(n−1)

Interval	2020​-2929	3030​-3939	4040​-4949	5050​-5959	6060​-6969	7070​-7979
Frequency	11	2121	4040	2020	88	55

Standard

deviationequals=11.011.0

​(Round to one decimal place as​ needed.)

Answer 1

Solution:

given that,

Class (1)	Frequency (f) (2)	Mid value (x) (3)	d=x-Ah=x-5054.5*1010 A=5054.5,h=1010 (4)	f⋅d (5)	f* (6)
2020 - 2029	11	2024.5	-3	-33	99
3030 - 3039	2121	3034.5	-2	-4242	8484
4040 - 4049	4040	4044.5	-1	-4040	4040
5050 - 5059	2020	5054.5	0	0	0
6060 - 6069	88	6064.5	1	88	88
7070 - 7079	55	7074.5	2	110	220
---	---	---	---	---	---
	n=8335	-----	-----	∑f⋅d=-8117	∑f*=12931

Solution:

Sample Standard deviation

=√0.6031*1010

=0.7766*1010

=784.366

=784.4