Question

the following are the ages of 12 physics teachers in a school district. 29, 30, 32, 33, 36, 39, 49, 51, 52, 52, 56, 57 notice that the ages are ordered from least to greatest. give the five - number summary and the interquartile range for the data set. five - number summary minimum: lower quartile: median: upper quartile: maximum: interquartile range:

Explanation:

Step1: Find minimum and maximum

The minimum is the smallest value and maximum is the largest. Given data set: 29, 30, 32, 33, 36, 39, 49, 51, 52, 52, 56, 57. Minimum = 29, Maximum = 57.

Step2: Calculate the median

Since there are $n = 12$ data - points, the median is the average of the $\frac{n}{2}=6$th and $\frac{n}{2}+1 = 7$th ordered values. Median=$\frac{39 + 49}{2}=44$.

Step3: Find the lower half and lower quartile

The lower half of the data is 29, 30, 32, 33, 36, 39. Since there are 6 values, the lower - quartile ($Q_1$) is the average of the 3rd and 4th ordered values. $Q_1=\frac{32+33}{2}=32.5$.

Step4: Find the upper half and upper quartile

The upper half of the data is 49, 51, 52, 52, 56, 57. Since there are 6 values, the upper - quartile ($Q_3$) is the average of the 3rd and 4th ordered values. $Q_3=\frac{52 + 52}{2}=52$.

Step5: Calculate the inter - quartile range

Inter - quartile range (IQR)=$Q_3 - Q_1$. IQR=$52-32.5 = 19.5$.

Answer:

Minimum: 29
Lower quartile: 32.5
Median: 44
Upper quartile: 52
Maximum: 57
Interquartile range: 19.5