The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these observations are 2,3,5,10,11,13,15,21, then the mean deviation about the median of all the 10 observ

Question

The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these observations are 2,3,5,10,11,13,15,21, then the mean deviation about the median of all the 10 observations is [2026]

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(4)

$\frac{2 + 3 + 5 + 10 + 11 + 13 + 15 + 21 + a + b}{10} = 9$

$\frac{80 + a + b}{10} = 9 \Rightarrow a + b = 10 . . . (1)$

$\frac{\sum x_{i}^{2}}{10} - {(\frac{\sum x_{i}}{10})}^{2} = 34.2$

$\frac{2^{2} + 3^{2} + 5^{2} + 10^{2} + 11^{2} + 13^{2} + 15^{2} + 21^{2} + a^{2} + b^{2}}{10} - {(9)}^{2} = 34.2$

$\frac{1094 + a^{2} + b^{2}}{10} - 81 = 34.2$

$1094 + a^{2} + b^{2} - 810 = 342$

$a^{2} + b^{2} = 58 . . . (2)$

$a = 7, b = 3 or a = 3, b = 7$

$Numbers = 2, 3, 5, 7, 10, 11, 13, 15, 21$

$Mean = \frac{7 + 10}{2} = 8.5$

$M.D. = \frac{6.5 + 5.5 + 5.5 + 3.5 + 1.5 + 1.5 + 2.5 + 4.5 + 6.5 + 12.5}{10}$

$= \frac{50}{5}$

$= 5$

Solution

Q.
The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these observations are 2,3,5,10,11,13,15,21, then the mean deviation about the median of all the 10 observations is [2026]

1 6

2 7

3 4

4 5

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Solution

Q. The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these observations are 2,3,5,10,11,13,15,21, then the mean deviation about the median of all the 10 observations is [2026]

1 6

2 7

3 4

4 5

Want Us to Email you About Special Offers & Updates?

Q.
The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these observations are 2,3,5,10,11,13,15,21, then the mean deviation about the median of all the 10 observations is [2026]