Question

If the mean of the observations a, a+6, a+2 , a+8 and a+4 is 11, find (i) the value of 'a' (ii) the median

Answer 1

Answer:

i)a=-5

9

ii)a+2

Step-by-step explanation:

1)

5a+20=11

=>5a=11-20

=>5a=-9

=>a=5 =>a=-5

-9 9

2) Median=Middle term

=>a,a+6,a+2,a+8,a+4

(1)(2) (3) (4) (5)

=>Median=a+2

Answer 2

(i) The value of a is 7.

(ii) The median is 11.

Step-by-step explanation:

Given : If the mean of the observations a, a+6, a+2 , a+8 and a+4 is 11.

To find : (i) the value of 'a' (ii) the median ?

Solution :

(i) Mean is defined as the sum of observation divided by total number of observation.

i.e. $M=\frac{\sum x_n}{n}$

Substituting the values,

$11=\frac{a+a+6+a+2+a+8+a+4}{5}$

$55=5a+20$

$5a=55-20$

$5a=35$

$a=\frac{35}{5}$

$a=7$

The value of a is 7.

The observations became, 7,7+6,7+2,7+8,7+4

i.e. 7,13,9,15,11

(ii) Arranging into ascending order,

7,9,11,13,15

The median is defined as the central value of observation.

As observations are odd in numbers i.e. 5.

$\text{Median}=\frac{n+1}{2}^{th}\text{ term}$

$\text{Median}=\frac{5+1}{2}^{th}\text{ term}$

$\text{Median}=3^{rd}\text{ term}$

$\text{Median}=11$

Therefore, the median is 1.

#Learn more

The mean of 10 observations is 7 & the mean of 15 observations is12 then mean of all the observations

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