Chapter 10.1, Problem 20HP

To determine

To evaluate an example with mode greater than mean and median.

Explanation of Solution

Given information:

Mode is greater than mean and median.

Formula used:

Mean formula is,

  

Where, f is frequency

N is total number of items

X is item.

Median formula is,

  

Where, N cumulative frequency

Mode formula is,

  $Mode=ObservationWithHighestFrequency$

Consider the dataset,

Person	Salary	Cumulative frequency
Ross	10	10
Chandler	20	30
Joey	10	40
Racheal	20	60
Monica	50	110
Phoebe	80	190
Total	190

For Mode,

Substituting the highest value of the given dataset,

  $Mode=80$

For mean, substituting the values,

  $\overline{X}=\frac{190}{6}$

On solving,

  $\overline{X}=31.66$

Hence, mean= 31.66

For median, substituting the values,

  $M=\frac{(190+1)}{2}term$

So,

  $M=\frac{191}{2}$

On solving,

  $M=95.5$

Comparing the value with the table.

So, median is 50.

Comparing, mean, median and mode.

Mode of the given dataset is greater than mean and median both. Therefore, the given dataset is and example of a dataset, where, mode is greater than mean and median.