Question

ann records the number of students in a variety of classes at her school. the results are shown below in order from least to greatest.
20, 23, 23, 24, 26, 28, 30, 31
suppose that the class with 30 students changes to 26 students.. answer the following.
(a) what happens to the interquartile range (iqr)?
the iqr increases by \\(\square\\) students.
the iqr decreases by \\(\square\\) students.
the iqr stays the same.
(b) what happens to the range?
the range increases by \\(\square\\) students.
the range decreases by \\(\square\\) students.
the range stays the same.

Explanation:

Step1: Find original IQR

First, split original data: 20,23,23,24 | 26,28,30,31
$Q_1 = \frac{23+23}{2}=23$, $Q_3 = \frac{28+30}{2}=29$
$IQR_{original}=29-23=6$

Step2: Find new data IQR

New data: 20,23,23,24,26,26,28,31
Split: 20,23,23,24 | 26,26,28,31
$Q_1 = \frac{23+23}{2}=23$, $Q_3 = \frac{26+28}{2}=27$
$IQR_{new}=27-23=4$

Step3: Compare IQR values

$6-4=2$, so IQR decreases by 2.

Step4: Find original range

$Range_{original}=31-20=11$

Step5: Find new range

$Range_{new}=31-20=11$

Step6: Compare range values

$11-11=0$, so range stays same.

Answer:

(a) The IQR decreases by 2 students.
(b) The range stays the same.