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Statistics and set problems

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Statistics and set problems

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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

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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,
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Quote:
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.

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