Question

A researcher records the following data for the number of different food items chosen by seven participants in a buffet-style setting: 1, 6, 2, 5, 4, 3, and 7. Is the mean equal to the median in this example

Answer 1

Yes.

Explanation:

Given:

A researcher records the following data for the number of different food items chosen by seven participants in a buffet-style setting: 1, 6, 2, 5, 4, 3, and 7.

Question asked:

Is the mean equal to the median in this example ?

Solution:

First of all we will calculate mean the median and then compare between these two:-

As we know:

`Mean=(Sum\ of\ observations )/(Number\ of\ observations)`

`=(1+6+2+5+4+3+7)/(7) \\\\=(28)/(7) =4`

Mean = 4

To find median, first we will order these as ascending order:

1, 6, 2, 5, 4, 3, 7 = 1, 2, 3, 4, 5, 6, 7

For odd number of observations,

`Median=(n+1)/(2),\ n=Number\ of\ observations`

`=(7+1)/(2) =(8)/(2) =4`

That means, fourth term will be the median

Median = 4

We found that mean and median both are 4.

Thus, yes mean and median both are equal in this example.