Question

The mean of 11 observation is 65. If the mean of first 6 observations is 63 and that of last six is 66. Findthe sixth observation

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The sixth observation is 59.

Step-by-step explanation:

Since we have given that

Number of observation = 11

Mean = 65

So, it becomes,

$\dfrac{\sum x_i}{11}=65\\\\\sum x_i=715$

mean of first six observations = 63

So, it becomes,

$\dfrac{x_1+x_2+x_3+x_4+x_5+x_6}{6}=63\\\\x_1+x_2+x_3+x_4+x_5+x_6=63\times 6\\\\x_1+x_2+x_3+x_4+x_5+x_6=378$

mean of last six observations = 66

So, it becomes,

$\dfrac{x_6+x_7+x_8+x_9+x_{10}+x_{11}}{6}=63\\\\x_6+x_7+x_8+x_9+x_{10}+x_{11}=66\times 6\\\\x_6+x_7+x_8+x_9+x_{10}+x_{11}=396$

Now, we have given that

$x_1+x_2+x_3+x_4+x_5+x_6+x_6+x_7+x_8+x_9+x_{10}+x_{11}=378+396=774\\\\x_1+x_2+x_3+x_4+x_5+2x_6+x_7+x_8+x_9+x_{10}+x_{11}=774\\\\x_1+x_2+x_3+x_4+x_5+x_6+x_7+x_8+x_9+x_{10}+x_{11}=715$

So, subtracting both the equations, we get that

$x_6=774-715=59$

Hence, the sixth observation is 59.

# learn more:

The mean of 11 observations is 50 . If the mean of first six observations i.s 49 and that of last six observations is 52 , then the sixth observation is

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