JEE MAIN - Mathematics (2021 - 20th July Evening Shift - No. 10)
If the mean and variance of six observations 7, 10, 11, 15, a, b are 10 and $${{20} \over 3}$$, respectively, then the value of | a $$-$$ b | is equal to :
9
11
7
1
Explanation
$$10 = {{7 + 10 + 11 + 15 + a + b} \over 6}$$
$$\Rightarrow$$ a + b = 17 ..... (i)
$${{20} \over 3} = {{{7^2} + {{10}^2} + {{11}^2} + {{15}^2} + {a^2} + {b^2}} \over 6} - {10^2}$$
a2 + b2 = 145 ...... (ii)
Solve (i) and (ii) a = 9, b = 8 or a = 8, b = 9
| a $$-$$ b | = 1
$$\Rightarrow$$ a + b = 17 ..... (i)
$${{20} \over 3} = {{{7^2} + {{10}^2} + {{11}^2} + {{15}^2} + {a^2} + {b^2}} \over 6} - {10^2}$$
a2 + b2 = 145 ...... (ii)
Solve (i) and (ii) a = 9, b = 8 or a = 8, b = 9
| a $$-$$ b | = 1
Comments (0)
