Statistics and set problems

This topic has expert replies
Moderator
Posts: 772
Joined: Wed Aug 30, 2017 6:29 pm
Followed by:6 members

Statistics and set problems

by BTGmoderatorRO » Thu Nov 02, 2017 11:01 am
During an experiment, the temperature of a liquid was measured several times. The temperatures, in degree Celsius, listed in increasing order, are 21, 25, x, 40, and 50. If the arithmetic mean of these temperatures is equal to the median, what is the value of x?

A. 34
B. 35
C. 36
D. 37
E. 38
OA is a

Can anyone help me here with approach to use in getting the best fit answer to the question? statistics is always a problem for me :cry:
Thank you so much for your help

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Thu Nov 02, 2017 1:35 pm
Hi Roland2rule,

We're given 5 numbers in INCREASING order: 21, 25, X, 40, and 50 and we're told that the AVERAGE of these temperatures is equal to the MEDIAN of the numbers. We're asked for the value of X.

The median of 5 numbers (in order) will be the 3rd number (in this case, since we know the 5 numbers are in INCREASING order, the median will be X). Since the average equals the median, we can set up the following equation:

(21+25+X+40+50)/5 = X
136+X = 5X
136 = 4X
34 = X

Final Answer: A

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image

User avatar
GMAT Instructor
Posts: 555
Joined: Wed Oct 04, 2017 4:18 pm
Thanked: 180 times
Followed by:12 members

by EconomistGMATTutor » Fri Nov 03, 2017 2:35 pm
During an experiment, the temperature of a liquid was measured several times. The temperatures, in degree Celsius, listed in increasing order, are 21, 25, x, 40, and 50. If the arithmetic mean of these temperatures is equal to the median, what is the value of x?

A. 34
B. 35
C. 36
D. 37
E. 38
OA is a

Can anyone help me here with approach to use in getting the best fit answer to the question? statistics is always a problem for me Crying or Very sad
Thank you so much for your help
Hi Roland2rule,
Let's take a look at your question.

The temperatures, in degree Celsius, listed in increasing order, are:
$$21,\ 25,\ X,\ 40,\ 50$$

We know that if we have odd number of values arranged in ascending or descending order, the middle value is known as median.
Hence, for the temperatures, listed in increasing order:
MEDIAN = X

Now, let's find the arithmetic mean of the temperatures.
Arithmetic Mean = Sum of Values / Number of Values
$$=\frac{\left(21+25+X+40+50\right)}{5}$$
$$=\frac{\left(136+X\right)}{5}$$

Th question states:
If the arithmetic mean of these temperatures is equal to the median, what is the value of x?
MEDIAN = ARITHMETIC MEAN
$$X=\frac{\left(136+X\right)}{5}$$
$$5X=136+X$$
$$5X-X=136$$
$$4X=136$$
$$X=\frac{136}{4}$$
$$X=34$$

Therefore, Option A is correct.

Hope it helps.
I am available if you'd like any follow up.
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

Image

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 7223
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Thu Oct 31, 2019 5:16 pm
BTGmoderatorRO wrote:During an experiment, the temperature of a liquid was measured several times. The temperatures, in degree Celsius, listed in increasing order, are 21, 25, x, 40, and 50. If the arithmetic mean of these temperatures is equal to the median, what is the value of x?

A. 34
B. 35
C. 36
D. 37
E. 38
OA is a

Can anyone help me here with approach to use in getting the best fit answer to the question? statistics is always a problem for me :cry:
Thank you so much for your help
We can create the equation:

(21 + 25 + x + 40 + 50)/5 = x

136 + x = 5x

136 = 4x

34 = x

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

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

ImageImage