henry recorded the number of miles he biked each day for a week. his miles were 25, 40, 35, 25, 40, 60, and…

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?

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?

Answer

Explanation:

Step1: Calculate the mean

The data set is (25, 40, 35, 25, 40, 60, 75). The mean (\bar{x}=\frac{25 + 40+35 + 25+40+60+75}{7}=\frac{300}{7}\approx42.86)

Step2: Calculate the squared - differences

((25 - 42.86)^2=( - 17.86)^2 = 318.98) ((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 = 318.98) ((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)

Step3: Calculate the variance

The variance (s^{2}=\frac{318.98+8.18 + 61.78+318.98+8.18+293.78+1032.98}{7 - 1}=\frac{2043.86}{6}\approx340.64)

Step4: Calculate the standard deviation

The standard deviation (s=\sqrt{340.64}\approx18.5)

Answer:

(18.5)