Question

Find the IQR (interquartile range). 19, 21, 18, 17, 18, 22,46

Answer 1

Answer:

4.

Step-by-step explanation:

Step 1: Formula.

$IQR=Q3-Q1$

--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Step 2: Explain/define.

• The interquartile range is the difference between quartile 3 and quartile 1.
• Quartile 1 is the median of the upper half of a data set.
• Quartile 3 is the median of the lower half of a data set.
• The median is the 'middle value.'

--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Step 3: Order/arrange.

In order to find the median, you must first put the numbers in numerical order.

19, 21, 18, 17, 18, 22, 46

               ↓

17, 18, 18, 19, 21, 22, 46

The lower half of the data set, not including the median of the whole data set, is 17, 18, and 18.

The upper half of the data set is 21, 22, and 46.

--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Step 4: Solve.

• 17, 18, 18

• 21, 22, 36

Next, we find the medians of both sets.

The median of the lower half is 18 (Q1).

The median of the upper half is 22 (Q3).

Lastly, we subtract Q3 from Q1.

$22-18=4.$

--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Step 5: Conclude.

I, therefore, believe the interquartile range of this data set is 4.