What is the Standard Deviation correct up to two decimal places) of the numbers: 21334, 21335, 21336,
21337 and 21338?
Answers
Given :- What is the Standard Deviation correct up to two decimal places) of the numbers: 21334, 21335, 21336, 21337 and 21338 ?
Solution :-
Standard Deviation Step by step :-
Step 1 :work out the arithmetic mean of the numbers .
- Total numbers = 5.
- Sum = 21334 + 21335 + 21336 + 21337 + 21338 = 106680.
- Arithmetic mean = Sum / Total numbers = (106680/5) = 21336. { Or, mean is middle number. }
Step 2 :Take each number, subtract the mean and square the result .
Differences (Every Number minus Mean) :-
- (21334 - 21336) = (-2) => 4
- (21335 - 21336) = (-1) => 1
- (21336 - 21336) = 0 => 0
- (21337 - 21336) = 1 => 1
- (21338 - 21336) = 2 => 4
Step 3 :- Now calculate the Variance .
- Sum of (Differences)² = 4 + 1 + 0 + 1 + 4 = 10
- Variance = (Sum of Differences)² / (Total numbers - 1) = 10 / (5 - 1) = 10 / 4 = 2.5 { when data is sample. }
Step 4 :- Take the square root of the Variance .
- Standard Deviation = √(Variance) = √(2.5) = 1.58 (Ans.)
Hence, Standard deviation of given numbers is 1.58.
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