Chapter 10.1, Problem 20HP

To determine

To verify: the data set can have more than one mode and median.

Answer to Problem 20HP

Any dataset can have more than one mode but can only have one median.

Explanation of Solution

Given information:

Need to verify that can dataset have more than one mode and median.

Mode: As mode represent the item of the data set which appears maximum time and there can be more than one number which can appear in the dataset for maximum and same number of times.

Consider the following examples having more than one mode.,

  $2,4,5,5,7,7,10$

  Mode = $5,7$

  $3,6,6,9,9,13,18,18$

  Mode = $6,9,18$

Median: Median represents the middle point of the data set. When data set have even numbers then average of two middle terms is calculated to determine median. So there can be only one median of dataset

Consider the following examples,

  $2,4,5,5,7,7,10$

Since number of data set is odd that is 7 so median is $4^{th}term$

Median = $5$

  $3,6,6,9,9,13,18,18$

Since number of data set is even that is 8 so median is $\left(\frac{4^{th}term+5^{th}term}{2}\right)$

  Median = $\left(\frac{9+9}{2}\right)$

   = $\left(\frac{18}{2}\right)$

   = $9$

Hence the data set can have more than one mode but only one median.