Median and Quartiles

Median and Quartiles

The median is a measure of central tendency that is calculated by arranging all the observations in a set in increasing order and finding the middle observation. The median is often used as a measure of central tendency for data sets that are not normally distributed.

The quartiles are measures of central tendency that divide the data set into four equal parts. The first quartile (Q1) is the middle observation of the lower half of the data set. The second quartile (Q2) is the median of the data set. The third quartile (Q3) is the middle observation of the upper half of the data set.

MCQs on Median and Quartiles

  1. What is the median?
  • A measure of central tendency that is calculated by arranging all the observations in a set in increasing order and finding the middle observation.
  • A measure of variability that is calculated by subtracting the smallest observation from the largest observation in a set.
  • A measure of skewness that is calculated by dividing the difference between the mean and the median by the standard deviation.
  • A measure of kurtosis that is calculated by dividing the fourth moment of a distribution by the fourth power of the standard deviation.

The correct answer is: A measure of central tendency that is calculated by arranging all the observations in a set in increasing order and finding the middle observation.

  1. What is the symbol for the median?
  • μ
  • σ
  • x̄
  • M

The correct answer is: M.

  1. What are the quartiles?
  • Measures of central tendency that divide the data set into four equal parts.
  • Measures of variability that are calculated by subtracting the smallest observation from the largest observation in a set.
  • Measures of skewness that are calculated by dividing the difference between the mean and the median by the standard deviation.
  • Measures of kurtosis that are calculated by dividing the fourth moment of a distribution by the fourth power of the standard deviation.

The correct answer is: Measures of central tendency that divide the data set into four equal parts.

Tips for Using the Median and Quartiles

  • The median is a good measure of central tendency for data sets that are not normally distributed.
  • The quartiles can be used to identify the middle 50% of the data set.
  • The quartiles can be used to calculate the interquartile range (IQR), which is a measure of variability.