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QUESTION: 1

The mean of prime numbers between 20 and 30 is:

Solution:

The prime numbers between 20 and 30 are 23, 29.

► Mean of 23 and 29 = (23 + 29) / 2 = 52/ 2 = 26

QUESTION: 2

The arithmetic mean of 30 values is 69. The new mean, if each of the 30 values is increased by 5 is:

Solution:

Mean=30 then total sum=30×69=2070 if 5 increase to all then total sum=2070+30×5=2070+150=2220

New mean =2220÷30 =74

QUESTION: 3

In an examination, ten students scored the following marks: 60, 58, 90, 51, 47, 81, 70, 95, 87, 99. The range of this data is:

Solution:

The difference between the maximum & minimum value of the observation is called as **range**.

So Range = 99-47 = 52

QUESTION: 4

If the number of observations in a data set is 25 and the mean of the data is 32. Then, the sum of all observations is:

Solution:

The number of observation is 25. The mean is 32.

► The sum = 25 + 25 + 25... 32 times

► 32*25 = 800

QUESTION: 5

If the mean of 6, 4, 7, x and 10 is 8, the value of x is:

Solution:

Mean = sum of all obs. /no. of obs.

► 8 = (6+4+7+x+10)/5

► 40 = 27+x

► x = 13

QUESTION: 6

The maximum frequency is 10 for observation 4. Hence the mode of the data is:

Solution:

- The
**mode**is the most frequently occurring value of data. - Here 4 is the most frequently occurring observation. So
**4**is the mode of the data.

QUESTION: 7

Median of the data 5, 9, 8, 6, 3, 5, 7, 12, 15 is:

Solution:

Arranging the given terms in **descending order** 15, 12, 9, 8, 7, 6, 5, 5, 3

► Number of terms = 9

► Median = **(n+1)/2** = 10/2 = 5^{th} term = 7

QUESTION: 8

Find median of following data: 83, 37, 70, 29, 45, 63, 41, 70, 34, 54:

Solution:

Arranging the data in ascending order, we have:

29, 34, 37, 41, 45, 54, 63, 70, 70, 83

Here, the number of observations, n = 10 (Even).

Hence, the median of the given data is **49.5**.

QUESTION: 9

What will be the mean of x, x + 2, x + 4, x + 6, x + 8, when the value of x is 12?

Solution:

► Mean = sum of all the obs./ no. of obs.

In the given question number of observation is 5.

► Sum of all observations = 5x + 20

But x =12; on substituting the value of x we get 5 * 12 + 20 = 80.

► Mean = 80 / 5 = 16

QUESTION: 10

The median of observations 17, 18, 20, 22, x+2, x+4, 31, 35, 37 is found to be 24. If the observations have been arranged in ascending order, the value of x will be:

Solution:

17, 18, 20, 22, x+2, x+4, 31, 35, 37

The total number of observation is 9, which is odd.

► Median = (9+1)/2^{th} term = 5^{th} term

Now 5^{th} term of the observation is (x+2)

Also given, median = 24

► x + 2 = 24

► x = 24-2

► x = 22

So the value of x is **22**.

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