Question

The mean deviation of the numbers 3, 4, 5, 6, 7 from mean is
A.25
B.5
C.1.2
D.9

Answer 1

Hint: As we know, mean is the average of data given in the question. So, to find meaning we have to sum up all the data and divide by the number of data. We can calculate mean by formula also, mean = $M = \dfrac{{\sum {{x_i}} }}{n}$ , where, ${x_i}$ is the data given and \[n\] is the number of terms.. The mean deviation about the mean is calculated by $\dfrac{{\sum {\left| {{x_i} - M} \right|} }}{n}$ . Now, put the value of mean in the formula and mean deviation about mean is obtained.

Complete step-by-step answer:
The data is given in the question.
The given data in the question is 3, 4, 5, 6, and 7.
To calculate the mean of the data, we have to observe the number of terms given.
There are 5 terms.
So, $n = 5$,
So, mean can be calculated by using the formula $M = \dfrac{{\sum {{x_i}} }}{n}$
Substituting values in the above formula,
$
\Rightarrow M = \dfrac{{3 + 4 + 5 + 6 + 7}}{5} \\
\Rightarrow M = \dfrac{{25}}{5} \\
\Rightarrow M = 5 \\
 $
So, the mean is 5
Now, to find mean deviation from mean the formula used is $\dfrac{{\sum {\left| {{x_i} - M} \right|} }}{n}$
Now substituting all the values in the above formula,
We get,
Mean deviation is
$ = \dfrac{{\left| {3 - 5} \right| + \left| {4 - 5} \right| + \left| {5 - 5} \right| + \left| {6 - 5} \right| + \left| {7 - 5} \right|}}{5}$
On simplifying,
$
   = \dfrac{{2 + 1 + 0 + 1 + 2}}{5} \\
   = \dfrac{6}{5} \\
   = 1.2 \\
 $

Therefore, mean deviation about mean is 1.2
Hence, the correct option is C.

Note: The mean deviation is also known as the mean absolute deviation. The calculation of mean and mean deviation about mean is simple but it should also be rechecked to avoid any mistakes in these types of questions.