Question

What is the third quartile of the following data set?

20, 21, 24, 25, 28, 29, 35, 36, 37, 43, 44

Answer 1

37.

Explanation:

The data is in ascending order, which is what we need to get the answer.

As there are 11 numbers the 9th number is the upper(third) quartile.

The median ( middle) number is 29 and the upper quartile is the middle number of the 5 numbers to the right of the median.

It is 37.

Answer 2

37

Explanation:

Before we find quartile, we have to arrange the data set in order first from least to greatest which this problem has already arranged the data for us.

Next, proceed with the calculation. The formula for finding position of quartile is:

`\displaystyle{Q_r = (r(N+1))/(4)}`

Where
`\displaystyle{Q_r}` means the rth quartile, N means number of data set. Since we want to find the third quartile, substitute r = 3 and there are 11 data so substitute N = 11:

`\displaystyle{Q_3 = (3(11+1))/(4)}\\\\\displaystyle{Q_3 = (3(12))/(4)}\\\\\displaystyle{Q_3 = 3\cdot 3}\\\\\displaystyle{Q_3 = 9}`

So the position of third quartile is at 9th position which is 37.

Henceforth, the third quartile is 37.