Question

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

Answer 1

Answer:

0.74

Step-by-step 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 = $\frac{(0.5 - 1.625)^{2} + (1.5 - 1.625)^{2}+ (2.0 - 1.625)^{2}+(2.5 - 1.625)^{2} }{4}$

Solving:

= $\frac{1.265625+0.015625+0.140625+0.765625}{4}$

= $\frac{2.1875}{4}$

σ² = 0.546875

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

$\sqrt{0.546875}$

= 0.73950997288745

= 0.74 (rounded)

hope this helps!