# Thread: interquartile range from frequency table

1. ## interquartile range from frequency table

I have attached a word document here (https://drive.google.com/open?id=1pF...7OLaGMio1BpmWt) with the frequency table along with my answer at the answer the textbook gives , only reason I ask is because i'm getting conflicting information on this example my answer is apparently wrong but on another question my method was used so what is going on?

q)Find the interquartile range for this data.
Ans)

Order the data -0,2,2,2,2,3,3,4,4

Q1=(9+1)/4=2.5 which then =2

Q3=3(9+1)/4=7.5 which then =3.5

So 3.5-2 =1.5 is the iqr

Firstly find, cumulative frequency

Cf=22

So Q1=(22+1)/4=5.75 which then= game 2

And Q3=3(22+1)/4=17.25= game 8

8-2=6

So interquartile range =6 games

2. Hey Falcon9, welcome to the forum!

Although I don't claim to understand the cumulative frequency method, I can tell you that what you are doing in your solution is wrong, just at a glance. For one thing, you state your answer as 6 games, which leads me to believe you've forgotten which row of numbers in the table is the actual data set. The data set is not the game numbers, but the number of goals per game. So your answer should be a number of goals. Also, at a glance, the answer cannot possibly be 6, because the highest number of goals scored is 4, and the lowest number of goals scored is 0. So the max-min spread of the data set is 4. The interquartile range, which is also a measure of the spread of the data, cannot possibly be higher than 4. It certainly can't be six!

If you give some thinking as to what interquartile range actually means, and why you are computing it (i.e. what is it useful for? What does it tell you about the data?), then you can arrive at an answer by inspection. The quartiles Q1 through Q3 are three numbers that divide the data set into four equal groups: the lowest 25%, the next highest 25%, the next highest 25%, and the highest 25%. So the first quartile (Q1) is the 25th percentile: 25% of the data values are at or below this value. The second quartile (Q2) is the 50th percentile: 50% of the values are at or below this value. It's also known as the median: it splits the data set in half. The third quartile (Q3) is the 75th percentile: 75% of the data set values are at or below this value, while 25% of them are above it.

Knowing this, I can split up the ordered data set just at a glance. The median (Q2) is just the middle "2" in the list (in bold):

(0,2,2,2),2,(3,3,4,4)

Q2 = 2

To find Q1, I just take this lower half, and find its middle value (median):

(0,2,2,2)

Well there are an even number of values here (four of them), so the median is just the average of the 2nd and 3rd number in the list. Both of those numbers are 2, so their average is 2.

Q1 = 2 (this value splits off the lowest 25% from the highest 75%)

To find Q3, I just take the upper half, and find its middle value (median):

(3,3,4,4)

Well there are an even number of values here (four of them), so the median is just the average of the 2nd and 3rd number in the list. That's (3+4)/2 = 3.5

Q3 = 3.5 (this value splits off the highest 25% from the lowest 75%)

IQR = Q3 - Q1 = 3.5 - 2 = 1.5

The interquartile range is a measure of the spread or variation of the data. If it is large, the number of goals varies a lot from game to game. If it is small, the number of goals is pretty consistent from game to game.

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