Question

the Arithmetic mean of grouped data. x, x + 1, x + 5, x + 10 and x + 14 is 20 then x is
A) 12
B) 14
C) 10
D) 20
​

Answer 1

Given :-

Arthemetic mean of x , x+1 , x+ 5 , x+ 10 , x + 14 is 20

To find :-

Value of x

Solution:-

${Arthemetic \: mean} = \dfrac{Sum\:of\:observations}{No\:of\:observations}$

Sum of observations = x +(x + 1) + (x + 5) + (x + 10) +( x + 14)

Sum of observations = x + x + 1 + x + 5 + x + 10 + x + 14

Sum of observations = 5x + 30

No.of observations = 5

Now Finding Arthemetic mean,

${Arthemetic \: mean} = \dfrac{Sum\:of\:observations}{No\:of\:observations}$

${20} = \dfrac{5x + 30}{5}$

$20 \times 5 = 5x + 30$

$100 = 5x + 30$

$100 - 30 = 5x$

$5x = 70$

$x = \dfrac{70}{5}$

$\bigstar \underline{\boxed{x= 14}}$

Verification:-

Then the Required data will be ,

x , x+ 1, x +5 , x +10 , x +14

x = 14

x + 1 = 15

x + 5 = 19

x + 10 = 24

x + 14 = 28

Data is 14, 15, 19, 24 , 28

So, for this data mean should be 20

${Mean} = \dfrac{14+15+19+24+28}{5}$

${Mean}=\dfrac{100}{5}$

Mean of data= 20

$\bigstar \underline{\boxed{LHS=RHS}}$

$\bigstar \underline{\boxed{Verified!}}$

Know more :-

Mean of the data :- Sum of observations/No.of observations Mean or average same

Mode of the data :- Most frequently repeated number that means which number appears more

Median of data :- Middle most number of the data

Range of the data :- Range is nothing but difference of maximum value and minimum value