Question

Q1 - Prove that if 15 is added to items in a series, the mean value of series is increased by 15.

Q2 - Find out the median of following series. Marks 2, 7, 9, 3, 2, 2, 3, 5, 6.

Q3 - Find out the mode of following series. Marks 2, 3, 3, 2, 2, 2, 7, 7, 7, 3, 3, 2, 2, 2.​

Answer 1

Solution: 1

We need to prove that the mean value of series is increased by 15 when 15 is added to items.

Now,

Let assume the data of the students according to their marks.

Name of students Marks obtained

Shyam 4

Ram 6

Nidhi 3

Shaan 7

Niti 5

★ Mean = ΣX/N ★

→ X-bar = 4 + 6 + 3 + 7 + 5/5 = 25/5 = 5

•°• Old mean = 5

• It is given in the question if 15 is added to items in series

Name of students Marks obtained

Shyam 4 + 15 = 19

Ram 6 + 15 = 21

Nidhi 3 + 15 = 18

Shaan 7 + 15 = 22

Niti 5 + 15 = 20

★ Mean = ΣX/N ★

→ X-bar = 19+21+18+22+20/5 = 100/5 =20

•°• New mean = 20

→ Increase in mean

→ New mean - old mean

→ 20 - 5

→ 15

Conclusion : If any specific value is added in different items in a series, then the mean value of series is increased by the same specific value.

________________________________

Solution: 2

Marks series → 2, 7, 9, 3, 2, 2, 3, 5, 6.

• Arrange all the values in ascending order

→ 2, 2, 2, 3, 3, 5, 6, 7, 9

• As we know that

★ Median for odd = (N + 1/2)th term Where "N" is the number of terms

• N = 9

→ (9 + 1/2)th term

→ (10/2)the term

→ 5th term

•°• Median (M) = 5th term = 3

________________________________

Solution : 3

Series → 2, 3, 3, 2, 2, 2, 7, 7, 7, 3, 3, 2, 2, 2.

• Arrange in ascending order

→ 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 7, 7, 7

→ The value that occurs mostly = 2

•°• Mode (Z) = 2

________________________________