## Related questions with answers

The article "Can We Really Walk Straight?" (Amer. J. Phys. Anthropol., 1992: 19-27) reported on an experiment in which each of 20 healthy men was asked to walk as straight as possible to a target $60 {m}$ away at normal speed. Consider the following observations on cadence (number of strides per second):

$\begin{array}{llllllllll}.95 & .85 & .92 & .95 & .93 & .86 & 1.00 & .92 & .85 & .81\end{array}$

$\begin{array}{llllllllll}.78 & .93 & .93 & 1.05 & .93 & 1.06 & 1.06 & .96 & .81 & .96\end{array}$

Use the methods developed in this chapter to summarize the data; include an interpretation or discussion wherever appropriate.

Solution

VerifiedWe will use various methods described in this chapter to describe the given data.

Firstly we will sort the given sample:

$\begin{align*} [0.78,\; 0.81,\; 0.81,\; 0.85,\; 0.85,\; 0.86,\; 0.92,\; 0.92,\; 0.93,\; 0.93,\;\\ 0.93,\; 0.93,\; 0.95,\; 0.95,\; 0.96,\; 0.96,\; 1.0,\; 1.05,\; 1.06,\; 1.06] \end{align*}$

$\textbf{\textcolor{#4257b2}{Sample mean}}$

The mean of a sample $x_1, x_2, ..., x_n$ is defined as:

$\begin{align*} \overline{x} = \frac{1}{n} \sum_{i=1}^{n} x_i \end{align*}$

Here we have a sample of a size $n = 20$, thus its mean is:

$\begin{align*} \overline{x} &= \frac{1}{n} \sum_{i=1}^{n} x_i\\ &= \frac{1}{20} \left[ 0.78+ 0.81+ ... + 1.06+ 1.06\right]\\ &= \boxed{0.926} \end{align*}$

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