The numbers 6, 8, 10, 12, 13 and x are arranged in an ascending order. If the mean of the observations is equal to the median, find the value of x. [3 MARKS]

Open in App

Solution

Formula: 1 Mark
Solution: 2 Marks

The numbers 6, 8, 10, 12, 13 and x are arranged in an ascending order.
Here n = 6, which is even.
$∴$ Median
$= \frac{{(\frac{n}{2})}^{t h} o b s e r v a t i o n + {(\frac{n}{2} + 1)}^{t h} o b s e r v a t i o n}{2}$
$= \frac{3^{r d} o b s e r v a t i o n + 4^{t h} o b s e r v a t i o n}{2}$
$= \frac{10 + 12}{2} = 11$
Mean $= \frac{S u m o f o b s e r v a t i o n s}{N o . o f o b s e r v a t i o n s}$
$= \frac{6 + 8 + 10 + 12 + 13 + x}{6} = \frac{49 + x}{6}$
According to question,
Mean = Median
$\Rightarrow \frac{49 + x}{6} = 11$
$\Rightarrow 49 + x = 66 \Rightarrow x = 17$

Suggest Corrections

Similar questions

26, 29, 42, 53, x, x + 2, 70, 75, 82, 93

65,

x

The following observations are arranged in ascending order:
26, 29, 42, 53, x, x + 2, 70, 75, 82, 93.
If fife median is 65, find the value of x.

11, 12, 14, (x - 2), (x + 4), (x + 9), 32, 38, 47

24

x

Join BYJU'S Learning Program