Question

using technology to calculate standard deviation
henry recorded the number of miles he biked each day for a week. his miles were 25, 40, 35, 25, 40, 60, and 75. enter the data into the statistics calculator.
what is the standard deviation of the miles henry biked to the nearest tenth?

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{25 + 40+35 + 25+40+60+75}{7}=\frac{300}{7}\approx42.86$

Step2: Calculate the variance

The variance $s^{2}=\frac{(25 - 42.86)^{2}+(40 - 42.86)^{2}+(35 - 42.86)^{2}+(25 - 42.86)^{2}+(40 - 42.86)^{2}+(60 - 42.86)^{2}+(75 - 42.86)^{2}}{7 - 1}$
First, calculate each term:
$(25 - 42.86)^{2}=(-17.86)^{2}=319.06$
$(40 - 42.86)^{2}=(-2.86)^{2}=8.18$
$(35 - 42.86)^{2}=(-7.86)^{2}=61.78$
$(25 - 42.86)^{2}=(-17.86)^{2}=319.06$
$(40 - 42.86)^{2}=(-2.86)^{2}=8.18$
$(60 - 42.86)^{2}=(17.14)^{2}=293.78$
$(75 - 42.86)^{2}=(32.14)^{2}=1032.98$
Sum of these terms: $319.06+8.18+61.78+319.06+8.18+293.78+1032.98 = 2043.02$
Variance $s^{2}=\frac{2043.02}{6}\approx340.50$

Step3: Calculate the standard deviation

Standard deviation $s=\sqrt{340.50}\approx18.5$

Answer:

$18.5$