Question

Listed below are the measured radiation absorption rates (in W/kg) corresponding to 11 cell phones . Use the given data to construct a boxplot and identify the 5-number summary 1.25 1.41 0.99 1.33 0.67 1.49 0.98 0.63 1.42 0.58 1.23

Answer 1

The 5-number summary is 0.58, 0.67, 1.23, 1.41 and 1.49, all in W/kg

Step-by-step explanation

Firstly, we arrange the given data in ascending order as follows

0.58 0.63 0.67 0.98 0.99 1.23 1.25 1.33 1.41 1.42 1.49

The five-number summary is the minimum, first quartile, median, third quartile, and maximum.

Note: The number of observations, N = 11

The minimum = 0.58

The first quartile, Q₁ = 1/4(N+1) = 1/4 (11+1) = 1/4 (12) = 3, Therefore, the first quartile is the 3rd number = 0.67

The median = 1/2(N+1) = 1/2 (11 +1) = 1/2 (12) = 6. Hence the median is the 6th number = 1.23

The third quartile, Q₃ = 3/4 (N + 1) = 3/4 (11 + 1) = 3/4 (12) = 9. Therefore, the third quartile is the 9th number = 1.41

Lastly, the maximum = 1.49