Question

If the mean of the data 3,21, 25, 17, (x+ 3), 19, (x- 4) is 18, find the value of x. Using this value of x, find the mode of the data.

Answer 1

ANSWER:
We know that,
Mean =Sum of observations/Number of observations
The given data is $3,21,25,17,(x+3),19,(x–4).$
Mean of the given data $=\frac{3+21+25+17+x+3+19+x-4}{7}$
⇒$18\times 7=84+2x$
⇒$126-84=2x$
⇒$2x=42$

⇒$x=21$
Hence, the value of x is 21.
Now, the given data is 3, 21, 25, 17, 24, 19, 17
Arranging this data in ascending order:
3, 17, 17, 19, 21, 24, 25
Here, 17 occurs maximum number of times.
∴ Mode = 17
Hence, the mode of the data is 17.