shrutib wrote:how to attack the Data Sufficiency questions regarding mean, median, range and Standard Deviation. Specially the type where they ask whether mean and median are same?

Thank you

Hi Shruti,

This is a very common doubt and an important concept.

Mean = Median when:

1. the set consists of evenly spaced numbers
2. if all the members of the set are equal
3. set has just one number
4. One more case

Let's discuss the point # 4.

We've already seen that for every set of evenly spaced numbers (or an Arithmetic Progression), Mean = Median.

BUT

If Mean = Median for a set of numbers, then the set of numbers need not be an AP.

Let me show some sets of numbers which are not in an AP but for which mean = median:

(i) 2, 3, 5, 7, 8
(ii) 3, 4, 4, 4, 5
(ii) 1, 4, 5, 6, 7, 8, 11

Your turn now! Can you show me a few such sets of numbers?

Hint: Take any AP. Tweak a few terms in it so that neither the Mean nor the Median change and it no longer remains an AP.

aneesh.kg wrote:

shrutib wrote:how to attack the Data Sufficiency questions regarding mean, median, range and Standard Deviation. Specially the type where they ask whether mean and median are same?

Thank you

Hi Shruti,

This is a very common doubt and an important concept.

Mean = Median when:

1. the set consists of evenly spaced numbers
2. if all the members of the set are equal
3. set has just one number
4. One more case

Let's discuss the point # 4.

We've already seen that for every set of evenly spaced numbers (or an Arithmetic Progression), Mean = Median.

BUT

If Mean = Median for a set of numbers, then the set of numbers need not be an AP.

Let me show some sets of numbers which are not in an AP but for which mean = median:

(i) 2, 3, 5, 7, 8
(ii) 3, 4, 4, 4, 5
(ii) 1, 4, 5, 6, 7, 8, 11

Your turn now! Can you show me a few such sets of numbers?

Hint: Take any AP. Tweak a few terms in it so that neither the Mean nor the Median change and it no longer remains an AP.

Aneesh,
your point 4 is an extension of the 1 only. Isnt it?

Gaurav 2013-fall wrote: Aneesh,
your point 4 is an extension of the 1 only. Isnt it?

Hi Gaurav,

Point 4 is a manipulation of Point 4, if that's what you mean by 'extension'. You can manipulate a set of evenly spaced integers such that its Median and Mean do not change as shown in the examples in the previous post.

Anurag@Gurome wrote: The mean and median of a set are are same when,
1. All the elements of the set are uniformly distributed around the mean. For example, {1, 2, 3, 4, 5} or {1, 2, 7, 12, 13} etc.
2. The set contains only one element.
3. All the elements of a set are same.

2 and 3 are special cases of 1.

Hi Anurag,
I would beg to differ with your point no. 1. In my opinion, the numbers need not be uniformly distributed about the mean for mean = median.
For example:
2, 9, 10, 12, 17 does not have terms uniformly distributed about the mean ( which is 10) and yet mean = median.
I think uniform distribution is just a special case. Please correct me if I am wrong.