Question

What is the standard deviation of the data? 0.5 1.5 2.0 2.5

Answer 1

0.74

Explanation:

The standard deviation of a data set is the sqaure root of the variance, so first we must find the variance. The equation for variance is:

σ² =
`\frac{{(x_(1)-[x bar] )}^(2)+...+{(x_(n)-[x bar]) }^(2)}{n}`

x = number in the data set
xbar = median of the data set
n = number of terms

Plugging in the given values, the equation for the variance of this number set is:

σ² =
`((0.5 - 1.625)^(2) + (1.5 - 1.625)^(2)+ (2.0 - 1.625)^(2)+(2.5 - 1.625)^(2) )/(4)`

Solving:

=
`(1.265625+0.015625+0.140625+0.765625)/(4)`

=
`(2.1875)/(4)`

σ² = 0.546875

Since the standard devianation is the sqaure root of the variance, we'll sqaure 0.546875:

`√(0.546875)`

= 0.73950997288745

= 0.74 (rounded)

hope this helps!

Answer 2

0.5

Step-by-step explanation
Because it is a standar deviation