Question

13. The mean of a, b, c, d and e is 28. If the mean of a, c, and e is 24, what is the mean of
band d?
(a) 31
(b) 32
(c) 33
(d) 34​

Answer 1

Given:

• The mean of a, b, c, d and e is 28.
• The mean of a, c and e is 24.

To find: The mean of b and d.

Answer:

The mean is the average of the data set. The formula to find the mean is as follows:

$\sf Mean = \dfrac{Sum\ of\ the\ observations}{Number\ of\ observations}$

As per the question, we know that $\sf \dfrac{a\ +\ b\ +\ c\ +\ d\ +\ e}{5}\ =\ 28$ . From it,

$\sf a\ +\ b\ +\ c\ +\ d\ +\ e\ =\ 28\ \times\ 5\\\\\bf a\ +\ b\ +\ c\ +\ d\ +\ e\ =\ 140$

We also know that $\sf \dfrac{a\ +\ c\ +\ e}{3}\ =\ 24$.  From it,

$\sf a\ +\ c\ +\ e\ =\ 24\ \times\ 3\\\\\bf a\ +\ c\ +\ e\ =\ 72$

From both these equations, we consider that

$\sf a\ +\ b\ +\ c\ +\ d\ +\ e\ =\ 140\\\\(a\ +\ c\ +\ e)\ +\ b\ +\ d\ =\ 140\\\\72\ +\ b\ +\ d\ =\ 140\\\\b\ +\ d\ =\ 140\ -\ 72\\\\\bf b\ +\ d\ =\ 68$

Since we know the formula to find the mean, let's use the final equation above to do so.

$\sf Mean\ of\ b\ and\ d\ =\ \dfrac{68}{2}\\\\\\\bf Mean\ of\ b\ and\ d\ =\ 34$

Therefore, the mean of b and d is 34.