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. 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 30​-39 40​-49 50​-59 60​-69 70​-79 80​-89 90​-99 Frequency 1 2 4 2 18 32 37 Standard deviationequals nothing ​(Round to one decimal place as​ needed.)

Answer 1

Answer : Standard deviation = 12.8

Mid points(X)	Frequency(f)	Freq*X	(X-mean)	(X-mean)2	f*(X-mean)2
34.5	1	34.5	-48.958	2396.918	2396.918
44.5	2	89	-38.958	1517.752	3035.503
54.5	4	218	-28.958	838.585	3354.34
64.5	2	129	-18.958	359.418	718.837
74.5	18	1341	-8.958	80.252	1444.531
84.5	32	2704	1.042	1.085	34.722
94.5	37	3496.5	11.042	121.918	4510.981
Total ->	96	8012	-	-	15495.833

Standard deviation = sqrt ( f*(X-mean)² / (n -1))

=sqrt ( 15495.833) / (96 - 1)

= 12 .772

Standard deviation = 12.8