Question

PLEASE I NEED HELP ASAP

Find the standard deviation of the given data rounded to the nearest hundredth. 5.6, 5.2, 4.6, 4.9, 5.7, 6.4​

Answer 1

Standard deviation = 0.59

Explanation:

Given data → 5.6, 5.2, 4.6, 4.9, 5.7, 6.4

Mean of the given data =
`(5.6+5.2+4.6+4.9+5.7+6.4)/(6)`

= 5.4

Data (x) (x - mean) (x - mean)²

5.6 5.6 - 5.4 = 0.2 (0.2)² = 0.04

5.2 5.2 - 5.4 = -0.2 (-0.2)² = 0.04

4.6 4.6 - 5.4 = -0.8 (-0.8)² = 0.64

4.9 4.9 - 5.4 = -0.5 (-0.5)² = 0.25

5.7 5.7 - 5.4 = -0.3 (-0.3)² = 0.09

6.4 6.4 - 5.4 = 1 (1)² = 1

N = 6
`\sum (x-mean)^2` = 2.06

Since, Standard deviation =
`\sqrt{(\sum (x-mean)^2)/(N)}`

=
`\sqrt{(2.06)/(6) }`

= 0.5859

≈ 0.59