Question: Boxplot-Based Conclusions

Comment on Boxplot-Based Conclusions

can you explain statement c more briefly please.
greenlight-admin's picture

Sure thing. The 4 different parts of the Set A boxplot each represent 1/4 of the data. So, each part represents 100 data points. In the boxpot, the 3rd quartile is at 8, so we can conclude that the 100 values in that rightmost part are greater than or equal to 8. So, statement C is true.
Does that help?

I'm still not understanding this explanation. How does the 4 different parts of the Set A boxplot each represent 1/4 of the data? Also how can we conclude that the 100 values in the rightmost part are greater than or equal to 8?
greenlight-admin's picture

I'll refer you to the lesson on boxplots: https://www.greenlighttestprep.com/module/gre-statistics/video/1364

We first divide the 400 values into 200 upper and 200 lesser numbers.
Then we find the medians of the upper and lesser numbers, and use those medians to divide the upper and lesser values into halves (of 100 each).

For answer choice C, first notice that the boxplot tells us that 3rd quartile is 8
This means the median of the upper numbers is 8

There are two possible cases in which the median of the upper values is 8:
i) none of the upper values = 8.
This means the median, 8, is calculated by finding the average of the two middlemost upper values.
This means 8 divides the 200 upper values into two equal sets, which means half are greater than 8 and half are less than 8
This means statement C is true

ii) at least two of the upper values are 8, and these two values are the middlemost values.
If the two 8's are the middlemost values, then there are MORE than 100 values that are greater than or EQUAL TO 8.
This means statement C is true

Does that help?

If you're uncertain, try to create a set that meets Set A's boxplot yet shows that statement C is false.

Cheers,
Brent

Hi Brent, a quick question. Always in any box-plot, the four different parts of it represent 1/4 of the data?
Thanks.
greenlight-admin's picture

Sometimes they represent exactly 1/4 of the data, and sometimes they represent approximately 1/4 of the data. See the examples at https://www.greenlighttestprep.com/module/gre-statistics/video/1364

Great! Thanks.

Could you explain the statement B, please? Basically, I don't get the possibility of being 5 (median)by an average of two five. As you explained, if the number of data set is even then the median must be an average of two middle numbers. And the median divides a set of data into two equal parts.
greenlight-admin's picture

Glad to help.

There are 400 values in Set B.

Since we have an EVEN number of values, the median will be the average of the two middle values (when the values are arranged in ascending order).

That is, the median = (term_200 + term_201)/2

The boxplot tells us that the median = 5, so we can say: (term_200 + term_201)/2 = 5

One possible scenario is that term_200 = 4 and term_201 = 6, in which case there are EXACTLY 200 terms greater than 5

Another possible scenario is that term_200 = 5 and term_201 = 5, in which case there are FEWER THAN 200 terms greater than 5.

Why is this?

In order to have EXACTLY 200 terms greater than 5, then we need EVERY term from term_201 to term 400 to be greater than 5.
However, if term_201 = 5, then term_201 is NOT greater than 5, which means there are FEWER THAN 200 terms greater than 5

Does that help?

Cheers,
Brent

In regards to C being a correct answer, is it not possible that the same median possibility that made B incorrect happened at Q3?
greenlight-admin's picture

Be careful. Statement B refers to Set B, and statement C refers to Set A.

Cheers,
Brent

The definition of quartiles specified that the data is divided into four "roughly-equal" groups... so how can we conclude that at least 100 values will be greater than or equal to 8 (option C)? If the 4 quartiles are only roughly equal, isn't it possible that this 4th quartile actually has less than 100 values?
greenlight-admin's picture

The phrase "roughly equal" refers to instances when the number of values isn't divisible by 4
Since we have 400 values, each quartile will have 100 values.

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