Question

If $\overline X - Z = 3$ and $\overline X + Z = 45$ then find $\overline X $
A) 2
B) 23
C) 24
D) 26

Answer 1

Hint: This is the concept of mean, mode. Mean$ = \overline X $ & Mode$ = Z$.
Definition of the mean: The mean is also known as an average, is obtained by dividing the sum of observed values by the number of observations.
Definition of the mode: The mode of a set of data is the value which occurs most frequently

Complete step-by-step answer:
Here we have given two equations.
$\overline X - Z = 3$ ………(1)
$\overline X + Z = 45$………(2)
We have to find $\overline X $.
For that we can do addition of (1) & (2) equations.
Let us do the addition.
$ \Rightarrow \overline X - Z + \overline X + Z = 3 + 45$
Simplify it.
$ \Rightarrow 2\overline X = 48$
To find mean we have to divide by 2 on both sides.
So, we will get,
 $ \Rightarrow \overline X = 24$
$\therefore $ Mean $ = 24$

So, the correct answer is “Option C”.

Note: With mode & mean students should be aware of the concept is median.
Definition of the median: The middle number; found by ordering all data points & picking out the one which is in the middle.