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Question 1 Mean Median And Mode Of Ungrouped Data Exercise 18A

Find the mean of:

(i) the first eight natural numbers

(ii) the first ten odd numbers

(iii) the first seven multiples of 5

(iv) all the factors of 20

(v) all prime numbers between 50 and 80.

Answer:

(i) We know that

First eight natural numbers = 1, 2, 3, 4, 5, 6, 7 and 8

So we get

Mean = sum of numbers/ total numbers

By substituting the values

Mean = (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8)/8

On further calculation

Mean = 36/8

By division

Mean = 4.5

Therefore, the mean of the first eight natural numbers is 4.5.

(ii) We know that

First ten odd numbers = 1, 3, 5, 7, 9, 11, 13, 15, 17 and 19

So we get

Mean = sum of numbers/ total numbers

By substituting the values

Mean = (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19)/10

On further calculation

Mean = 100/10

By division

Mean = 10

Therefore, the mean of first ten odd numbers is 10.

(iii) We know that

First seven multiples of five = 5, 10, 15, 20, 25, 30 and 35

So we get

Mean = sum of numbers/ total numbers

By substituting the values

Mean = (5 + 10 + 15 + 20 + 25 + 30 + 35)/7

On further calculation

Mean = 140/7

By division

Mean = 20

Therefore, the mean of first seven multiples of five is 20.

(iv) We know that

All the factors of 20 = 1, 2, 4, 5, 10 and 20

So we get

Mean = sum of numbers/ total numbers

By substituting the values

Mean = (1 + 2 + 4 + 5 + 10 + 20)/6

On further calculation

Mean = 42/6

By division

Mean = 7

Therefore, the mean of all the factors of 20 is 7.

(v) We know that

All prime numbers between 50 and 80 = 53, 59, 61, 67, 71, 73 and 79

So we get

Mean = sum of numbers/ total numbers

By substituting the values

Mean = (53 + 59 + 61 + 67 + 71 + 73 + 79)/7

On further calculation

Mean = 463/7

So we get

Mean = 66*1/7

Therefore, the mean of all prime numbers between 50 and 80 is 66*1/7.

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