Exam 4: Descriptive Statistical Measures

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For grouped data, mean, $\bar{x}=\frac{\sum_{i=1}^{n} f_{i} x_{i}}{n}$ , where $n$ is the number of observations, and $f_{l} \mathrm{x}_{j}$ is individual frequencies multiplied by the corresponding number of days.

$\begin{array}{|l|l|l|}\hline \begin{array}{l}\text { Female } \\\text { Customer } \\\text { Frequency }\end{array} & & \\\hline & & \\\hline \text { Days (x) } & \begin{array}{l}\text { Frequency } \\(\mathbf{x})\end{array} & \text { Frequency* Days } \\\hline 1 & 0 & 0 \\\hline 2 & 5 & 10 \\\hline 3 & 8 & 24 \\\hline 4 & 11 & 44 \\\hline 5 & 18 & 90 \\\hline \text { Sum } & 42 & 168 \\\hline & & \\\hline & \text { Mean } & 4 \\\hline\end{array}$

First we multiply individual frequencies by their corresponding number of day. Then we add the multiplied values to ohtain $\sum_{i=1}^{n} f_{i} x_{i}$ .

Here,
$\sum_{i=1}^{n} f_{i} x_{i}=168$
$n$ is calculated to be 42 .
Therefore the mean, $\bar{x}=168 / 42=4$ . $\bar{x}=4$ .