If the numbers 3, 5, 7, 4 have frequencies x, x+4, x-3, x+8 with their arithmetic mean of 4, then x will be _____.

$\frac{5}{3}$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

$\frac{7}{4}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$\frac{2}{3}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$\frac{11}{3}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A
$\frac{5}{3}$

Given:
$\begin{matrix} x_{i} & 3 & 5 & 7 & 4 f_{i} & x & x + 4 & x - 3 & x + 8 \end{matrix}$
$∴ \sum x_{i} f_{i} = 3 x + 5 (x + 4) + 7 (x - 3) + 4 (x + 8) = 3 x + 5 x + 20 + 7 x - 21 + 4 x + 32 = 19 x + 31 \dots (i)$
and $\sum f_{i} = x + x + 4 + x - 3 + x + 8 = 4 x + 9 \dots (i i)$
Given $\frac{\sum f_{i} x_{i}}{\sum f_{i}} = 4 \Rightarrow \frac{19 x + 31}{4 x + 9} = 4$
[From Eqs.(i) and (ii)]
$\Rightarrow 19 x + 31 = 16 x + 36 \Rightarrow 3 x = 5 ∴ x = \frac{5}{3}$

Suggest Corrections

Similar questions

x, x + 4, x - 3, x + 8

x

3, 5, 7, 4

x, x + 4, x - 3, x + 8.

4

x

If the numbers 3, 5, 7, 4 have frequencies x, x+4, x-3, x+8 with their arithmetic mean of 4, then x will be _____.

If the observations 3, 5, 7, 4 have frequencies x, x+4, x-3, x+8 respectively and mean of these observations is 4, then find the value of 'x'.

4

9

x

(x - 1)

6

x

Join BYJU'S Learning Program