Question

here are yesterdays high temperatures (in fahrenheit) in 12 u.s. cities. 48, 58, 62, 64, 65, 66, 66, 73, 73, 75, 77, 82 notice that the temperatures are ordered from least to greatest. give the five - number summary and the interquartile range for the data set. five - number summary minimum: first quartile: median: third quartile: maximum: interquartile range:

Explanation:

Step1: Identify minimum

The smallest value is 48.

Step2: Calculate position of first - quartile

$n = 12$, position of $Q_1=\frac{1}{4}(n + 1)=\frac{1}{4}(12 + 1)=3.25$. The first - quartile is the value between the 3rd and 4th ordered values. So $Q_1=\frac{62+64}{2}=62$.

Step3: Calculate position of median

Position of median for $n = 12$ is $\frac{n}{2}=6$ and $\frac{n}{2}+1 = 7$. Median is $\frac{66 + 66}{2}=66$.

Step4: Calculate position of third - quartile

Position of $Q_3=\frac{3}{4}(n + 1)=\frac{3}{4}(12+1)=9.75$. The third - quartile is the value between the 9th and 10th ordered values. So $Q_3=\frac{73+73}{2}=73$.

Step5: Identify maximum

The largest value is 82.

Step6: Calculate inter - quartile range

$IQR=Q_3 - Q_1=73 - 62 = 11$.

Answer:

Minimum: 48
First quartile: 62
Median: 66
Third quartile: 73
Maximum: 82
Interquartile range: 11