HOW DO I BREAK THIS QUESTION DOWN?

Question

Jessica’s Spanish test scores are 98, 74, 88, 83, 91, and 85. Find the range, median, first and third quartiles, and interquartile range of her scores. Use the measures of variation to describe the data. (SHOW WORK)

Answer 1

Hello Abby,

This answer supplements Stephanie’s helpful answer with additional information. Please read Stephanie's answer first and then continue here. I hope this helps!

INTERQUARTILE RANGE

To get the interquartile range, we subtract the first quartile (83, as shown in Stephanie’s answer) from the third quartile (91, as shown in Stephanie’s answer).

Interquartile Range = Third Quartile - First Quartile

Interquartile Range = 91 - 83

Interquartile Range = 8

Your answer is 8.

Are you wondering what this means? 

You can think of the interquartile range as the range of the middle half of the scores. In this example, the interquartile range tells us the range of the middle half of Jessica's Spanish test scores. Had Jessica gotten a terrible score one day, or a perfect score one day, that score would not change her interquartile range.

MEASURES OF VARIATION

The original question asks us to "use the measures of variation to describe the data." 

The word "data," in this example, refers to Jessica's Spanish test scores: 98, 74, 88, 83, 91, and 85.

If you can tell us the range (as described in Stephanie's answer) and the interquartile range (shown in my answer), these are both measures of variation. Each of these answers tell us something about the variation in Jessica's Spanish test scores.

Keep up the good learning!

Answer 2

RANGE

To find the range we simply take largest number minus smallest number. The largest number is 98 and the smallest is 74. So we have 98-74=24.

MEDIAN

The median is just the middle number. We will start by ordering the six numbers from smallest to largest as follows: 74, 83, 85, 88, 91, 98. Since we have 6 numbers (which is even), the median will be the average of the two middle numbers--85 and 88. (Note that if we had an odd number on values we would simply take the middle value. So the average of 85 and 88 is just (85+88)/2=86.5.

FIRST QUARTILE

Since our median is not an actual value in our data set, to find the first quartile we can take the median of the lower half of our values (74, 83, 85). The median is the middle value which is clearly 83, so this is our first quartile.

THIRD QUARTILE

To find the third quartile we can take the median of the upper half of our values (88, 91, 98). The median is the middle value which is clearly 91, so this is our third quartile.