In 7-9, find the mean, median, range, and interquartile...

In $7-9,$ find the mean, median, range, and interquartile range for each set of data to the nearest tenth.
$$
\begin{array}{|c|c|}\hline x_{i} & {f_{i}} \\ \hline 11 & {5} \\ {16} & {8} \\ {19} & {9} \\ {31} & {6} \\ {37} & {5} \\ {32} & {5} \\ {35} & {6} \\ \hline\end{array}
$$

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Key Concepts

Frequency Distribution

A frequency distribution summarizes data by showing the number of observations (or frequency) associated with each distinct value or interval. It is useful for organizing data, especially when the dataset includes repeated values, and provides a clear view of how values are distributed.

Interquartile Range

The interquartile range (IQR) is a measure of spread that represents the difference between the upper (75th percentile) and lower (25th percentile) quartiles. It reflects the dispersion of the middle 50% of the data, giving a more resistant assessment of variability that minimizes the influence of outliers.

Range

The range is a measure of variability that is calculated as the difference between the largest and smallest values in the dataset. It provides a simple indication of the spread of the data.

Median

The median is the middle value in an ordered dataset, which divides the data into two equal parts. It is particularly useful when the data contains outliers, as it is less affected by extreme values than the mean.

Mean

The mean is a measure of central tendency calculated by summing all values in the dataset and dividing by the total number of values. It provides a numerical average that represents the central value of the data distribution.

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