Question

in the data set below, what are the lower quartile, the median, and the upper quartile?
41 90 26 92 63 85 98 59 67 86
lower quartile =
median =
upper quartile =

Explanation:

Step1: Sort the data set

First, sort the data set in ascending order: $26,41,59,63,67,85,86,90,92,98$

Step2: Find the median

Since there are $n = 10$ data points. The median is the average of the $\frac{n}{2}$-th and $(\frac{n}{2}+1)$-th values. $\frac{n}{2}=5$, $\frac{n}{2}+1 = 6$. The 5 - th value is $67$ and the 6 - th value is $85$. Median $=\frac{67 + 85}{2}=\frac{152}{2}=76$

Step3: Find the lower quartile

The lower half of the data is $26,41,59,63,67$. Since there are $n_1=5$ data points in the lower half. The lower quartile is the 3 - rd value. Lower quartile $=59$

Step4: Find the upper quartile

The upper half of the data is $85,86,90,92,98$. Since there are $n_2 = 5$ data points in the upper half. The upper quartile is the 3 - rd value. Upper quartile $=90$

Answer:

lower quartile $=59$, median $=76$, upper quartile $=90$