Question

The mean of 7 numbers x-3,x+2,x,9,x-2,x+1,13 is 10 .then find the value of x

Answer 1

Find the sum of the 7 numbers:

Given that the mean of the 7 numbers is 10

Sum of the 7 numbers = 7 x 10 = 70

Find the sum of the number in term of x:

(x - 3) + (x + 2) + x + 9 + (x - 2) + (x + 1) + 13

= x - 3 + x + 2 + x + 9 + x - 2 + x + 1 + 13

= 5x + 20

Solve x:

Sum = 5x + 20

Sum = 70

5x + 20 = 70

5x = 50

x = 10

Answer: x = 10

Answer 2

Answer :


$given \: mean \: = 10 \\ \\ as \: we \: know \: that \: \\ \\ mean \: = \: \frac{sum \: of \: observations}{total \: number \: of \: observations} \\ \\ so \: we \: can \: assume \: that \\ \\ 10 = \frac{sum \: of \: observations}{total \: number \: of \: observations} \\ \\ sum \: of \: observations \: = \:( x - 3 )+ (x + 2) + (x) +( 9) + (x - 2) + (x + 1) + (13) \\ \\ = 5x + 20 \\ \\ total \: number \: of \: observations \: = 7$
$therefore \\ \\ 10 = \frac{5x + 20}{7} \\ \\ or \: \: \frac{5x + 20}{7} = 10 \\ \\ 5x + 20 = 10 \times 7 \\ \\ 5x + 20 = 70 \\ \\ 5x = 70 - 20 \\ \\ 5x = 50 \\ \\ x = \frac{50}{5} \\ \\ x = 10 \\ \\ so \: \: \: x \: = 10 \\ \\ therefore \\ \\ x - 3 = 10 - 3= 7 \\ \\ x + 2 = 10 + 2 = 12 \\ \\ x - 2 = 10 - 2 = 8 \\ \\ x + 1 = 10 + 1 = 11$



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