Question

the following are the ages of 14 history teachers in a school district. 27, 29, 32, 34, 36, 44, 44, 45, 46, 46, 52, 53, 54, 57 notice that the ages are ordered from least to greatest. give the interquartile range for the data set. interquartile range:

Explanation:

Step1: Find the median (Q2)

Since there are $n = 14$ data - points, the median is the average of the 7th and 8th ordered values. $\text{Q2}=\frac{45 + 46}{2}=45.5$.

Step2: Find the lower half

The lower half consists of the first 7 values: $27,29,32,34,36,44,44$. The median of the lower half (Q1) is the 4th value. So, $\text{Q1}=34$.

Step3: Find the upper half

The upper half consists of the last 7 values: $46,52,53,54,57$. The median of the upper half (Q3) is the 4th value of this half. So, $\text{Q3}=53$.

Step4: Calculate the inter - quartile range (IQR)

$\text{IQR}=\text{Q3}-\text{Q1}=53 - 34=19$.

Answer:

19