Question

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: Calcular la media

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

Step2: Calcular las diferencias al cuadrado

$(25 - 42.86)^2=(- 17.86)^2 = 318.98$, $(40 - 42.86)^2=(-2.86)^2 = 8.18$, $(35 - 42.86)^2=(-7.86)^2 = 61.78$, $(25 - 42.86)^2=(- 17.86)^2 = 318.98$, $(40 - 42.86)^2=(-2.86)^2 = 8.18$, $(60 - 42.86)^2=(17.14)^2 = 293.78$, $(75 - 42.86)^2=(32.14)^2 = 1032.98$

Step3: Calcular la varianza

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

Step4: Calcular la desviación estándar

$s=\sqrt{340.64}\approx17.9$

Answer:

17.9