Question

find mean mode $ x of following observations arranged in ascending order if median is 62
29,32,48,50,x+1,x+3,72,78,84,95​

Answer 1

Given :-

• Observations are arranged in ascending order :-

29 , 32 , 48 , 50 , x + 1 , x + 3 , 72 , 78 , 84 , 95

• The mean of the given observation :- 62

Solution :-

Here,

Total number of observation = 10

As we know that,

10 is an even number. Even numbers are those numbers which are divisible by 2 .

Now,

By using the formula to find Median for even numbers :-

Median = (n/ 2)th obs+ ( n/2 + 1 )th obs / 2

According to the question,

The median of given observation = 62

Now,

Median

= (10/2)th obs + ( 10/2 + 1 )th obs / 2

62 = 5th obs + 6th obs / 2

Put the required values,

62 = x + 1 + x + 3 / 2

62 * 2 = 2x + 4

124 = 2 ( x + 2 )

124/2 = x + 2

62 = x + 2

x = 62 - 2 = 60

Thus,

• The value of 5th observations

= 60 + 1 = 61

• The value of 6th observation

= 60 + 3 = 63

Now,

We have to find mean

Mean = Sum of observation / Total observation

Mean = 29 + 32 + 48 + 50 + 61 + 63 + 72 + 78 + 84 + 95/ 10

Mean = 612/ 10

Mean = 61.2

Thus, The mean of the given data is 61.2

Here,

From the above data we observed that no observation is repeated

Thus, This data doesn't have mode

Hence, The mean and median of the above data is 61.2 and 62 $.$

Answer 2

$\huge \underline \mathfrak \red{❁Given❁}$

◆ Observations are arranged in ascending order :-

29 , 32 , 48 , 50 , x + 1 , x + 3 , 72 , 78 , 84 , 95

◆ The mean of the given observation :- 62

$\huge \underline \mathfrak \red{❁Solution❁}$

Here,

Total number of observation = 10

As we know that,

10 is an even number. Even numbers are those numbers which are divisible by 2 .

Now,

By using the formula to find Median for even numbers :-

Median = (n/ 2)th obs+ ( n/2 + 1 )th obs / 2

According to the question,

The median of given observation = 62

Now,

Median

= (10/2)th obs + ( 10/2 + 1 )th obs / 2

62 = 5th obs + 6th obs / 2

Put the required values,

62 = x + 1 + x + 3 / 2

62 * 2 = 2x + 4

124 = 2 ( x + 2 )

124/2 = x + 2

62 = x + 2

x = 62 - 2

x = 60

Thus,

◆ The value of 5th observations

= 60 + 1 = 61

◆The value of 6th observation

= 60 + 3 = 63

Now,

We have to find mean

Mean = Sum of observation / Total observation

Mean = 29 + 32 + 48 + 50 + 61 + 63 + 72 + 78 + 84 + 95/ 10

Mean = 612/ 10

Mean = 61.2

Thus, The mean of the given data is 61.2

Here,

From the above data we observed that no observation is repeated

Thus, This data doesn't have mode

Hence, The mean and median of the above data is 61.2 and 62