Question

The mean of 10 observations is 20 the mean of first six observation is 18 and that of last six observations is 21 The fifth observation is 12. Find the 6th observation

Answer 1

Answer:

The value of sixth observation is 22

Step-by-step explanation:

Given as :

The statement are

The mean of 10 observations is 20

i.e $x_1 + x_2 + x_3 + x_4 + ......... + x_10$ = 20 × 10

Or, $x_1 + x_2 + x_3 + x_4 + ......... + x_10$ = 200              ........A

Again

The mean of first six observation is 18

i.e $x_1+x_2+.....+x_6$ = 18 × 6

Or, $x_1+x_2+.....+x_6$ = 108                                       .........B

Similarly

The mean of last six observations is 21

i.e $x_5+x_6+x_7+...+x_10$ = 21 × 6

or, $x_5+x_6+x_7+...+x_10$ = 126                                ...........C

From A and B

$x_1+x_2+.....+x_6$ + $x_7+x_8+x_9+x_1_0$ = 200

i.e $x_7+x_8+x_9+x_1_0$ = 200 - 180

Or, $x_7+x_8+x_9+x_1_0$ = 92                                        ............D

From C and D

$x_5+x_6+x_7+...+x_10$ = 126

Or, $x_5+x_6$ + 92 = 126

Or, $x_5+x_6$ = 126 - 92

∴   $x_5+x_6$ = 34

Again

The fifth observation = $x_5$ = 12

So,$x_5+x_6$ = 34

Or, 12 + $x_6$ = 34

∴   $x_6$ = 34 - 12

i.e  $x_6$ = 22

So, The 6th observation = $x_6$ = 22

Hence, The value of sixth observation is 22 . Answer

Answer 2

Answer:

22

Step-by-step explanation:

Given as :

The statement are

The mean of 10 observations is 20

i.e.  = 20 × 10

Or,  = 200              ___A

Now,

The mean of first six observation is 18

i.e.  = 18 × 6

Or,  = 108                                       ___B

Similarly

The mean of last six observations is 21

i.e.  = 21 × 6

or,  = 126                                ___C

From A and B

+  = 200

i.e.  = 200 - 180

Or,  = 92                                   ___D

From C and D

= 126

Or,  + 92 = 126

Or,  = 126 - 92

∴    = 34

Again

The fifth observation =  = 12

So, = 34

Or, 12 +  = 34

∴    = 34 - 12

i.e.   = 22

So, The 6th observation =  = 22

Hence, The value of sixth observation is 22