If S = {0, 4, 5, 2, 11, 8}, how much greater than the

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Mon Mar 19, 2018 3:44 am

If S = {0, 4, 5, 2, 11, 8}, how much greater than the median of the numbers in S is the mean of the numbers in S?

(A) 0.5
(B) 1.0
(C) 1.5
(D) 2.0
(E) 2.5

The OA is A.

Experts, could you show me a fast way to solve this PS question? Please. I'd be thankful.

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Source: Beat The GMAT — Problem Solving | Mon Mar 19, 2018 3:44 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Mar 19, 2018 6:33 am

VJesus12 wrote:If S = {0, 4, 5, 2, 11, 8}, how much greater than the median of the numbers in S is the mean of the numbers in S?

(A) 0.5
(B) 1.0
(C) 1.5
(D) 2.0
(E) 2.5

To find the median, first arrange the values in ASCENDING ORDER: {0, 2, 4, 5, 8, 11}
Since the set has an EVEN number values, the median will be the average of the two middlemost numbers.
So, median = (4 + 5)/2 = 9/2 = 4.5

Mean = (sum of all values in the set)/(number of values in the set)
= (0 + 4 + 5 + 2 + 11 + 8)/6
= 30/6
= 5

How much greater than the median of the numbers in S is the mean of the numbers in S?
Median = 4.5
Mean = 5

The mean is 0.5 more than the median

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Tue Mar 20, 2018 4:06 pm

VJesus12 wrote:If S = {0, 4, 5, 2, 11, 8}, how much greater than the median of the numbers in S is the mean of the numbers in S?

(A) 0.5
(B) 1.0
(C) 1.5
(D) 2.0
(E) 2.5

Ordering the numbers from least to greatest we have:

0, 2, 4, 5, 8, 11

So the median of S is (4 + 5)/2 = 4.5.

The mean of S is (0 + 2 + 4 + 5 + 8 + 11)/6 = 30/6 = 5.

So the mean is 0.5 greater than the median.

Answer: A

Jeffrey Miller
Head of GMAT Instruction
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

by deloitte247 » Sat Mar 24, 2018 11:35 am

The median of a set with even number of elements is the average of two middle element when arranged in ascending order.
median;
S= {0,2,4,5,8,11}
median= $$\frac{\left(4+5\right)}{2}=\frac{9}{2}=4\ \frac{1}{2}$$

The mean of the set= $$\frac{\left(0+2+4+5+8+11\right)}{6}=\frac{30}{6}=5$$
The difference = 5 - 4.5= 0.5 $$\frac{\left(0+2+4+5+8+11\right)}{6}=\frac{30}{6}=5$$
$$Therefore,\ the\ mean\ is\ 0.5\ greater\ than\ the\ median.\ Hence\ option\ A\ is\ accurate$$

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