Question

given the data set: 10, 12, 14, 15, 16, 18, 21, 24, 27, 30 what range of values represents the middle 50% of the data? enter your values.

Explanation:

Step1: Find the median

The data - set has $n = 10$ values. The median is the average of the 5th and 6th ordered values. $\text{Median}=\frac{16 + 18}{2}=17$.

Step2: Split the data - set into two halves

The lower half is $10,12,14,15,16$ and the upper half is $18,21,24,27,30$.

Step3: Find the first quartile ($Q_1$)

The lower half has $n = 5$ values. The median of the lower half (first quartile) is the 3rd value. So, $Q_1 = 14$.

Step4: Find the third quartile ($Q_3$)

The upper half has $n = 5$ values. The median of the upper half (third quartile) is the 3rd value. So, $Q_3=24$.

Answer:

$14 - 24$