Statistics and set problems

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BTGmoderatorRO: Moderator; Posts: 772; Joined: Wed Aug 30, 2017 6:29 pmFollowed by: 6 members

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

Thank you so much for your help

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Source: Beat The GMAT — Problem Solving | Thu Nov 02, 2017 11:01 am

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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]

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EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pmFollowed by: 12 members; Thanked: 180 times

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
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Our average student improves 98 points.

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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
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]

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