Question

The table below shows data for a class's mid-term and final exams:

Mid-TermFinal
96 100
95 85
92 85
90 83
87 83
86 82
82 81
81 78
80 78
78 78
73 75
Which data set has the smallest IQR? (1 point)
Group of answer choices

They have the same IQR

Mid-term exams

Final exams

There is not enough information

Answer 1

The interquartile range is a measure of where the “middle fifty” is in a data set, where the bulk of the values lies.

The interquartile range formula is the first quartile subtracted from the third quartile:

`IQR=Q_3-Q_1`

IQR of the Mid-Term

Step 1: Arrange the numbers in order

`73,78,80,81,82,86,87,90,92,95,96`

Step 2: Find the median

`Median\Rightarrow86`

Step 3: Find Q1 and Q3

Q1 and Q3 are the median of the numbers before and after the median of the data set. Therefore, Q1 is the median of the first 5 numbers:

`Q_1=80`

Q3 is the median of the last 5 numbers:

`Q_3=92`

Step 4: Calculate the IQR

`IQR=92-80=12`

IQR of the Final

Step 1: Arrange the numbers in order

`75,78,78,78,81,82,83,83,85,85,100`

Step 2: Find the median

`Median\Rightarrow82`

Step 3: Find Q1 and Q3

Q1 and Q3 are the median of the numbers before and after the median of the data set. Therefore, Q1 is the median of the first 5 numbers:

`Q_1=78`

Q3 is the median of the last 5 numbers:

`Q_3=85`

Step 4: Calculate the IQR

`IQR=85-78=7`

ANSWER

The data with the smallest IQR is the FINAL.