Dispersion Statistics

Dispersion statistics are essential tools used to evaluate the variability or scatter of data points in a set. These measures include but are not limited to the range, variance, standard deviation, and the interquartile range. The basic purpose of these measures is to determine the degree of deviation from the central value. A high dispersion signifies a wide spread of values while a low dispersion indicates a close grouping of values.

Finding the Median

Consider the following set of numbers: 7, 13, 3, 5, 11, 4, 2. Calculate the median of this data set.

Finding the Mean (Arithmetic)

A survey of 5 people was conducted to find out how many books they read in a month. The results were: 3, 4, 8, 1, and 6. Calculate the mean and standard deviation.

Finding the Mode

Given a data set {5, 2, 9, 3, 5, 8, 5, 7, 2}, find the mode of the set.

Finding the Standard Deviation

A random sample of 5 data points, 4, 6, 8, 10 and 12, was collected. Find the standard deviation of this sample.

Finding the Minimum

We have the data set {2,4,9,3,5,7,8,12,15,18}. Calculate the range, variance, and standard deviation, and then find the minimum among these calculated values.

Finding the Maximum

Given the dataset {5, 10, 15, 20, 25}. Calculate the maximum dispersion of the data set.

Finding the Lower or First Quartile

Consider the dataset [3, 5, 7, 8, 9, 11, 13, 15, 17, 19]. What is the first quartile (Q1) of this data set?

Finding the Upper or Third Quartile

Given the data set {3, 7, 8, 5, 12, 14, 21, 13, 18}, find the upper or third quartile (Q3).

Finding the Five Number Summary

Given the following set of data {7, 9, 13, 15, 16, 20, 21, 23, 24, 25, 29, 30, 31, 32, 33, 34, 36, 38, 43, 50}, find the five number summary (minimum, first quartile, median, third quartile, maximum).