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.
$$
\begin{array}{|c|c|}\hline x_{i} & {f_{i}} \\ \hline 50 & {3} \\ {45} & {8} \\ {40} & {12} \\ {35} & {15} \\ {30} & {11} \\ {25} & {7} \\ {20} & {4} \\ \hline\end{array}
$$

Key Concepts

Range

The range is a simple measure of variability calculated as the difference between the maximum and minimum values in the dataset. It provides a basic indication of the spread out or dispersion of the data but does not offer insights into the distribution of values between these extremes.

Interquartile Range (IQR)

The interquartile range (IQR) is a measure of variability that indicates the spread of the middle 50% of the data. It is calculated as the difference between the third quartile (the 75th percentile) and the first quartile (the 25th percentile). This metric is particularly useful for understanding the spread of the central portion of the data and is less affected by outliers.

Arithmetic Mean

The arithmetic mean is a measure of central tendency calculated by summing all the data values (often weighted by their frequencies) and then dividing by the total number of data points. In frequency distributions, each value is multiplied by its frequency to determine its contribution to the overall sum, and then that result is divided by the total frequency to yield the average value.

Median

The median is the middle value of a data set when the numbers are arranged in order. In the context of frequency distributions, the median is found by determining the cumulative frequencies and identifying the data point that splits the dataset into two equal halves, representing a central point of the data.

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