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.
• B. The actual mean temperture is ${26}^{\circ }C$
• C. The actual and incorrect mean temperature is ${25.2}^{\circ }C$
• D. The difference between actual mean temperature and incorrect mean temperature is ${0.8}^{\circ }C$.

Answer 1

Answer: (B), (D)

The difference between actual mean temperature and incorrect mean temperature is ${0.8}^{\circ }C$.

The mean of the given data will be calculated as,

$\begin{array}{cc}\text{Mean}& =\frac{\text{Sum of all data points}}{\text{Total number of data points}}\\ & =\frac{22+28+27+24+25}{5}\\ & =\frac{126}{5}\\ & =25.2\end{array}$

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 $26-22=4$ more.

That is, the actual sum of numbers will be,

$\begin{array}{cc}\text{Actual sum of temperatures}& =\text{Sum of temperatures with incorrect data}+4\\ & =126+4\\ & =130\end{array}$

Therefore, the actual mean will be calculated as,

$\begin{array}{cc}\text{Actual Mean}& =\frac{130}{5}\\ & =26\end{array}$

Hence, the difference between the actual mean and incorrect mean temperature is $26-25.2=0.8$.

So,the second and the last option are correct.