Sir I have the follwong tables, and need to show the Standard Deviation, the formula is also enclosed.
The tables are correct but I am having trouble figuring out the formula, please see below-
3. A company had 80 employees whose salaries are summarized in the frequency distribution below. Find the standard deviation. Find the standard deviation of the data summarized in the given frequency distribution.
Salary Number of Employees
5,001 -10,000 11
10,001 – 15,000 13
15,001 – 20,000 20
20,001 – 25,000 17
25,001 – 30,000 13
salaries frequencies class midpoint X f*x f*x^2
5001-10000 11 7500.5 82505.5 XXXXXXXXX 8
10001-15000 13 12500.5 162506.5 XXXXXXXXXX
15001-20000 20 17500.5 350010 XXXXXXXXXX
20001-25000 17 22500.5 382508.5 XXXXXXXXXX
25001-30000 13 27500.5 357506.5 XXXXXXXXXX
totals 74 (NNN) NNN-NNNNXXXXXXXXXXX
Variance 2 =
x2 f/n – ( xf/n) 2
4. The heights of a group of professional basketball players are summarized in the frequency distribution below. Find the standard deviation.
Height (in.) Frequency
70-71 4
72-73 9
74-75 18
76-77 11
78-79 9
80-81 4
82-83 1
heights frequency class midpoint x f*x f*x^2
70-71 4 70.5 282 19881
72-73 9 72.5 652.5 47306.25
74-75 18 74.5 1341 99904.5
76-77 11 76.5 841.5 64374.75
78-79 9 78.5 706.5 55460.25
80-81 4 80.5 322 25921
82-83 1 82.5 82.5 6806.25
totals 56 4228 319654
Variance 2 =
x2 f/n – ( xf/n) 2