Question

given the data set: 10, 12, 14, 15, 16, 18, 21, 24, 27, 30. what would happen to each measure on the box plot if 32 was added to the data? choose all that apply. a) the lower extreme and quartile 1 remain the same. b) the median decreases by 1. c) the median increases by 1. d) quartile 3 increases from 24 to 27. e) quartile 3 increases from 24 to 26. f) the upper extreme stays the same. g) the upper extreme increases from 30 to 32.

Explanation:

Step1: Analyze lower - extreme

The lower - extreme is the smallest value in the data set. Initially, it is 10. Adding 32 (a value larger than 10) does not change the smallest value. So the lower - extreme remains the same.

Step2: Analyze Quartile 1

Quartile 1 (Q1) is the median of the lower half of the data. The lower half of the original data set \(10,12,14,15,16\) has Q1 = 14. Adding 32 (a large value) does not affect the lower half of the data, so Q1 remains the same.

Step3: Analyze median

The original data set has \(n = 10\) values. The median is the average of the 5th and 6th ordered values, \(\frac{16 + 18}{2}=17\). After adding 32, the new data set has \(n = 11\) values, and the median is the 6th - ordered value. The ordered data set with 32 added is \(10,12,14,15,16,18,21,24,27,30,32\), and the median is 18. The median increases by \(18-17 = 1\).

Step4: Analyze Quartile 3

The upper half of the original data set \(18,21,24,27,30\) has Q3 = 24. After adding 32, the new upper - half data set \(21,24,27,30,32\) has Q3 = 27. So Q3 increases from 24 to 27.

Step5: Analyze upper - extreme

The upper - extreme is the largest value in the data set. Initially, it is 30. After adding 32, the new upper - extreme is 32.

Answer:

A. The lower extreme and Quartile 1 remain the same.
C. The median increases by 1.
D. Quartile 3 increases from 24 to 27.
G. The upper extreme increases from 30 to 32.