## Related questions with answers

Group Project: Collect the shoe size of everyone in the class. Use the sample means and variances and the types of plots presented in this chapter to summarize any features that draw a distinction between the distributions of shoe sizes for males and females. Do the same for the height of everyone in the class.

Solutions

VerifiedSHOE SIZE

Determine the shoe size of everyone in the class and record for every shoe size if it belongs to a male or a female.

$n$ is the number of values in the data set.

The mean is the sum of all values divided by the number of values:

$\overline{x}=\dfrac{\sum x_i}{n}$

The variance is the sum of squared deviations from the mean divided by $n-1$:

$s^2=\dfrac{\sum (x_i-\overline{x})^2}{n-1}$

You could create comparitive boxplots, dotplots, etc. For boxplots: The whiskers of the boxplot are at the minimum and maximum value. The box starts at the first quartile, ends at the third quartile and has a vertical line at the median. The first quartile is at 25% of the sorted data list, the median at 50% and the third quartile at 75%.

Compare the graphs, mean and variances for males and females.

The goal of the problem is to produce different statistics and plots concerning the shoe and height of the students. Below is a sample profile for $20$ students.

$\begin {array} {c|c|c|c} \text{Student No.} & \text{Shoe Size (cm)} &\text{Height (cm)} & \text{Gender}\\ \hline 1 & 18 & 101& F \\ 2 & 24 & 121 & F \\ 3 & 25 & 136 & F\\ 4 & 22 & 155 & F \\ 5 & 22 & 161 & F \\ 6 & 23 & 137 & F \\ 7 & 21 & 162 & F \\ 8 & 25 & 100 & F \\ 9 & 20 & 176 & F \\ 10 & 22 & 114 & F \\ 11 & 28 & 128 & M \\ 12 & 20 & 107 & M \\ 13 & 24 & 112 & M\\ 14 & 24 & 134 & M\\ 15 & 21 & 173 & M\\ 16 & 20 & 155 & M\\ 17 & 28 & 140 & M\\ 18 & 24 & 140 & M\\ 19 & 23 & 160 & M\\ 20 & 22 & 124 & M\\ \hline \end{array}$

$\small \text{Table 1. Details of Each Student}$

Note that the data was produced using a random generator.

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