Question

what is the third quartile of this data set? 21,24,25,28,29,35,37,39,42 a. 25 b. 38 c. 29 d. 24.5

Explanation:

Step1: Arrange data in order

The data set 21, 24, 25, 28, 29, 35, 37, 39, 42 is already in ascending - order.

Step2: Calculate position of third - quartile

The formula to find the position of the third - quartile ($Q_3$) for a data set of size $n$ is $i=\frac{3(n + 1)}{4}$. Here, $n = 9$. So, $i=\frac{3\times(9 + 1)}{4}=\frac{3\times10}{4}=7.5$.

Step3: Interpolate to find $Q_3$

Since the position $i = 7.5$, $Q_3$ is the value that is 0.5 of the way between the 7th and 8th ordered data values. The 7th value is 37 and the 8th value is 39. Using the interpolation formula $Q_3=x_7+(i - \lfloor i
floor)(x_8 - x_7)$, where $\lfloor i
floor$ is the greatest integer less than or equal to $i$. Here, $\lfloor7.5
floor = 7$. So, $Q_3=37+(7.5 - 7)\times(39 - 37)=37+0.5\times2 = 38$.

Answer:

B. 38