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Question

The temperature of a city was recorded for 5 consecutive days as follows:


And the average mean was calculated, however later on, it was found that the temperature on day I was 26 and not 22.

With respect to the given information, choose the correct options.

A
The actual mean temperature will be less than the mean recorded with incorrect entry of temperature.
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B
The actual mean temperture is 26C
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C
The actual and incorrect mean temperature is 25.2C
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D
The difference between actual mean temperature and incorrect mean temperature is 0.8C.
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Solution

The correct option is D The difference between actual mean temperature and incorrect mean temperature is 0.8C.
The mean of the given data will be calculated as,

Mean=Sum of all data pointsTotal number of data points=22+28+27+24+255=1265=25.2

Since, later on it was found that on day I the temperature was recorded wrong, therefore the data will be represented as,


As instead of 26, the temperature was recorded as 22, therefore the actual sum of all the data points will be 2622=4 more.

That is, the actual sum of numbers will be,

Actual sum of temperatures=Sum of temperatures with incorrect data+4=126+4=130

Therefore, the actual mean will be calculated as,

Actual Mean=1305=26

Hence, the difference between the actual mean and incorrect mean temperature is 2625.2=0.8.

So,the second and the last option are correct.

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