Given a set of numbers: {10, 11, 12, 15, 15, 15, 17, 19, 20, 20}. If a

Question

Given a set of numbers: {10, 11, 12, 15, 15, 15, 17, 19, 20, 20}. If a number 15 is included in the series, then which of the following will change?

I. Median 
II. Mode 
III. Standard deviation

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

LeoN88 · Answer

Mode will not change, earlier it was 15, now also it'll be 15. Mode= Element that occurs maximum number of times(Frequency).

Median will change, earlier it was 15.5, now 15
Old list 10, 11, 12, 15,  15, 15 , 17, 19, 20, 20
new list 10, 11, 12, 15, 15,  15,  15, 17, 19, 20, 20

VeritasKarishma   EgmatQuantExpert  could you help me how to quickly find whether there has been change in sd or not?

EDIT: Median won't change, new median= 15, old median (15+15)/2=15.

EgmatQuantExpert · Answer

Hey  LeoN88 ,
The value of standard deviation will change slightly, as the mean changes slightly.
If the mean of the original series was 15, then there would have been no change.

vishumangal · Answer

Hi,

Median wil not change as for old series also median is equal to 15. For even number terms we take the avg of values ( 15+15)/2

Posted from my mobile device

LeoN88 · Answer

Could you check once again.

old list has 15 and 15 in the middle so, median= mean of middlemost elements= 15.5

New list has 15 in the middle so median is 15.

vishumangal · Answer

Hi,if sum 15 +15 it comes out to be 30 and when you divide it by 2 that is 30/2 = 15

Posted from my mobile device

LeoN88 · Answer

Sorry, silly mistake mean of 15 and 15 is 15. You're right.

KarishmaB · Answer

In this question, I know that median and mode won't change. They were both 15 before and continue to be the same. So obviously, looking at the options, SD must change. There is no option that says none of the 3 quantities will change. Answer must be (C). That said, a trickier version of the question might need you to evaluate the change in SD. {10, 11, 12, 15, 15, 15, 17, 19, 20, 20} Note here that mean will be a bit more than 15. (since shortfall is 12 while extra is 16 assuming 15 to be the mean) When you add another 15 to it, the numerator will increase by a small quantity while the denominator will increase by 1. The SD will decrease slightly. You know this because when you add the same number to numerator and denominator of a number greater than 1, the number decreases and goes toward 1. If you want to keep the number same you need to add 'a' to numerator and 'b' denominator such that a is greater than b. For more on this, check: https://anaprep.com/number-properties-a ... nominator/ Another point, if the initial list's mean were 15, adding 15 to it would have certainly reduced the SD since numerator would not have changed while the denominator would have increased by 1. Check this video on SD: https://www.youtube.com/watch?v=0E6FQMzQVj0

Archit3110 · Answer

inclusion of 15 in the set will not change the median and mode but for SD ; i,e the variation of value along the mean will vary as we will have 1 more additional entry of the value ... 
IMO C

CrackverbalGMAT · Answer

This question is a moderately difficult question on Statistics. It tests your understanding of the statistical measures.

The median is the middle value (when there are an odd number of values), when all the values in the data set are arranged in ascending order/descending order. In case there are even number of values in the set, the median is the average of the two values in the middle.

The mode is that value that is seen most frequently in the data set.

Standard deviation is the root of the mean of the squared deviations, calculated with reference to the mean.

In this question, since there are 10 values, the median will be the average of the 5th and the 6th values. Since both these values are 15, the median = 15. 
When one more 15 is included in the set, the number of values in the set becomes 11 and the median becomes the 6th value. But the 6th value IS 15. Therefore, the median does not change. So, statement I should not be a part of the answer. Options A, D and E can be eliminated basis this.

In the set of values given, the number 15 occurs thrice and hence is the mode. When we introduce one more 15, the mode will still remain 15. Therefore, statement II is also not a part of the answer. Option B can be eliminated.

The correct answer option should be C.

The mean of the given set of values is  \frac{154}{10}  = 15.4. When another 15 is added, the mean reduces to  \frac{169}{11}  = 15.3. Because of this, the standard deviation is bound to change. Therefore, statement III only has to be the answer.

Remember that, the Standard deviation of a set of values always depends on the mean. You change things in a way it affects the mean, the standard deviation also gets affected.

On the timing front, this is a question which can be solved in about 1 minute.

Hope this helps!

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