Explanation

Recall that the range of the numbers in a group of data is the greatest number in the group minus the least number in the group. The table shows that the minimum height of the 80 students can vary from 140 to 144 centimeters, and the maximum height can vary from 160 to 164 centimeters. Thus the least possible range of the heights is 160 – 144, or 16 centimeters. The correct answer is Choice B.
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Hi Sandy,

Why the answer is not 20? (160-140)

Appreciate your help!

Thanks

Hi HarveyKlaus,

You are right it should be 20. or 160 - 140.

Regards
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So in this context the maximum possible range should be : 164-144 = 20? Or it should be : 164-140 = 24?

Hey yasir9909,

No that not correct. Range is the difference between the smallest and the largest measurement.

For example: 5,3,13,1,10

Range is 13-1 =12.

Now suppose you want to make it into a frequency distribution table with 4 classes say. Then width of each class would be range/no of classes, or \(\frac{12}{4}=3\).

Class	Frequency
1-4	2
5-8	1
9-12	1
13-16	1

So range is 13-1 or 16-4 = 12. As we know from the dataset
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But my question is still unanswered;what would be the maximum possible range of the heights of the 80 students according to this table?

I need to make my concept crystal clear on range in context of frequency distribution;though simple definition of range is quite straightforward :

Range = Maximum Value - minimum Value

No,

The limits of a frequency distribution table are not arbitrary as I have shown with the example above. They depend on the range of the data.

Range is: class width * no of classes = 4 * 5 for the original question
.............................................= 3 * 4 for the example in my post above,

So you can get the range from:

upper limit of first class - upper limit of the last class.

or

lower limit of first class - lower limit of the last class.
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Why can't it be 16????
if we consider the lowest height of six students is 144 and highest height is 160
then 160-144 = 16

Sonalika42 is right. For first row, its possible that all students have same height of 144 cms and for last row all students can have same height of 160 cms. Therefore least possible range is 160-44 = 16. Answer should be B

Hi phoenixio and Sonalika42,

Any frequency distribution has the information about the range within the table. I.e limits of each row is not arbitrary they are related to the range of the original dataset.

The range of the dataset is equally divided into classes. So it is quite possible that all the 6 students in 140 to 144 bracket are 144 cms and all 4 students in 160 to 164 is 160 cms. Then the range is 16. However the frequency distribution table would have had classes:

144 - 147
148 - 151
152 - 155
156 - 159
160 - 163

When you make a frequency distribution table the range information about the original dataset is not lost.

Regards
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thank you for replying Sandy
What i have understood from what you have said above is(pls correct me if i am wrong) that if the the distribution list has a range of 140-144 ,this range is not arbitrary ,it simply means that there is atleast one student with a height of 140cms else that range would not have begun with 140 ,it could have been any other value.
Is that what you are saying?
plzz do reply

No thats not what I am saying.

Range of a dataset in a frequency distribution is fixed: class size * number of classes.

Its possible all 4 have height 144 and then atleast one will have height 164. But the range remains 20.
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@ Sandy,

This is a question from ETS official guide and explanation from guide is as:

Recall that the range of the numbers in a group of data is the greatest number in the group minus
the least number in the group. The table shows that the minimum height of the 80 students can vary
from 140 to 144 centimeters, and the maximum height can vary from 160 to 164 centimeters. Thus
the least possible range of the heights is 160 – 144, or 16 centimeters. The correct answer is
Choice B.

I totally agree with Phoenixio

Sorry for the inconvenience. Maybe a typo by Sandy. Thank you guys for the feedback.

OA fixed
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Hey,

I know its the official solution and that was what I originally posted. However when I went back and checked the definitions from books there is no minimum/maximum range of a frequency distribution. When you make a table classes of the table are a function of the range of under lying dataset.

Here is another sample problem:



PS: Please look at the examples I am posting. I understand very clearly your argument for "minimum range". What I am trying to say is there is no such thing called a "minimum range" for a frequency distribution table.
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@ Sandy
i am getting what you are saying but my point was since no dataset was provided in the question ,we are free to assume that all 6 could be 144 and all 4 could be 160
its all about possibility.
the attachment which you have provided read step 3:-

Steps for constructing a frequency distribution from a data set
1. If the number of classes is not given, decide on a number of classes to use. This number should
be between 5 and 20.
2. Find the class width: Determine the range of the data and divide this by the number of classes.
Round up to the next convenient number (if it’s a whole number, also round up to the next
whole number).
3. Find the class limits: You can use the minimum data entry as the lower limit of the first
class. To get the lower limit of the next class, add the class width. Continue until you reach
the last class. Then find the upper limits of each class (since the classes cannot overlap, and
occasionally your data will include decimal numbers, remember that it’s fine for the upper
limits to be decimals).
4. Count the number of data entries for each class, and record the number in the row of the table
for that class. (The book recommends using “tally” marks to count)

@ Sandy
i agree with you when you say that there is no such thing as minimum range for a frequency distribution table, but in the given scenario its about how minimum can we make the range. And since no data set is provided we are at liberty to minimize the range.

i got really confused,
as you mentioned that range = greatest value- least value
so it should be 164-140= 24!!! plz answer me !!