Question

The following data shows Lakeisha's scores of five math quizzes. 100, 89, 84, 72, 95 What is the relationship between Lakeisha's mean and median quiz score?

Answer 1

Given :-

Lakeisha's scores of five math quizzes -

100, 89, 84, 72, 95

To Find :-

The relationship between Lakeisha's mean and median quiz score

Solution :-

First we have to arrange the given data in ascending or descending order.

The given scores in ascending order is -

72, 84, 89, 95, 100.

$\longrightarrow$ Mean = $\dfrac{\text{Sum\:\:of\:\:all\:\:observations}}{\text{Total\:\:no.\:\:of\:\:observations}}$

Here,

Sum of all observations = 72 + 84 + 89 + 95 + 100 = 440

Total number of observations = 5

So,

$\longrightarrow$ Mean of the given data = $\dfrac{440}{5} = 88$

Now, finding the median,

$\longrightarrow$ Median = $\left(\dfrac{n+1}{2}\right)th\:\:term$

Here,

n = Total number of observations = 5

So,

$\longrightarrow$ Median = $\left(\dfrac{5+1}{2}\right)th\:\:term= \left(\dfrac{6}{2} \right)th\:\:term=\left(3 \right)th\:\:term=89$

$\star$ The relationship between Lakeisha's mean and median quiz score is that the median of her scores is 1 greater than the mean of her score.