Question

Refer to the Table $2.23$. Find the third quartile. What is another name for the third quartile?

Short answer

The third quartile is represented by the number$4$, and it is also known as the$75th$percentile.

Step-by-step solution

Given

We are provided information on forty bus drivers who were asked how many hours they spend on their routes each day.

Explanation

Thepercentilesarethepartitionvaluesinstatistics.

The data is divided into $100$equal pieces by the percentile.

The median is represented by the 50th percentile, and $50\%$of the data is found below this figure.

In the same way, the $60th$percentile will contain $60\%$of the data below it.

The third quartile, or $75th$percentile, must be found.

We find $0.65$and $0.90$in the "cumulative relative frequency" column. We have 65 percent of the data when we have all twos and threes. We have $90\%$of the data if we include all four quadrants. As a result, the $75th$percentile must be$4.$

Another method to approach the problem is to calculate $75\%$of $40$, which equals $30.$

The 30th number in the third quartile, $Q3$, is $4.$

Countingvaluescanbeusedtoverifythisanswer.

(There are $29$values in the bottom quartile and ten in the top.)

$2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5$

Because the $30th$observation is definitely a $4$, the third quartile is also a $4$.

The $75th$percentile is another term for the third quartile.