2 Mark Question

Question 12 Marks

Find the mean of all factors of 10

Answer

The factors of 10 are 1, 2, 5 and 10.
Let $\bar{\text{x}}$ denote their arithmetic mean. Then,
$\bar{\text{x}}$ = (1 + 2 + 5 + 10) ÷ 4
= 18 ÷ 4
= 4.5

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Question 22 Marks

Find the mean of 994, 996, 998, 1002 and 1000.

Answer

Mean = Sum of the observations ÷ Total number of observations
Mean = (994 + 996 + 998 + 1002 + 1000) ÷ 5
= 4990 ÷ 5
= 998

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Question 32 Marks

Ashish studies for 4 hours, 5 hours and 3 hours on three consecutive days. How many hours does he study daily on an average?

Answer

Average number of study hours = (4 + 5 + 3) ÷ 3
= 12 ÷ 3
= 4 hours
Thus, Ashish studies for 4 hours on an average.

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Question 42 Marks

Find the mode of the data: 2, 6, 5, 3, 0, 3, 4, 3, 2, 4, 5, 2, 4

Answer

Arranging the data in ascending order such that same values are put together, we get:
0, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 6
Here, 2, 3 and 4 occur three times each. Therefore, 2, 3 and 4 are the three modes.

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Question 52 Marks

A cricketer scores the following runs in 8 innings: 58, 76, 40, 35, 48, 45, 0, 100. Find the mean score.

Answer

We have:
The mean score = (58 + 76 + 40 + 35 + 48 + 45 + 0 + 100) ÷ 8
= 402 ÷ 8
= 50.25 runs.

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Question 62 Marks

Find the mean of first five multiples of 3

Answer

The first five multiples of 3 are 3, 6, 9, 12 and 15.
Let $\bar{\text{x}}$ denote their arithmetic mean. Then,
$\bar{\text{x}}$ = (3 + 6 + 9 + 12 + 15) ÷ 5
= 45 ÷ 5
= 9

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Question 72 Marks

The marks (out of 100) obtained by a group of students in science test are 85, 76, 90, 84, 39, 48, 56, 95, 81 and 75. Find the
Mean marks obtained by the group.

Answer

In order to find the highest and lowest marks, let us arrange the marks in ascending order as follows:
39, 48, 56, 75, 76, 81, 84, 85, 90, 95
We have:
Mean marks = Sum of the marks ÷ Total number of students
Mean marks = (39 + 48 + 56 + 75 + 76 + 81 + 84 + 85 + 90 + 95) ÷ 10
= 729 ÷ 10
= 72.9.
Hence, the mean mark of the students is 72.9.

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Question 82 Marks

Find the mean of first five natural numbers.

Answer

The first five natural numbers are 1, 2, 3, 4 and 5.
Let $\bar{\text{x}}$ denote their arithmetic mean. Then,
$\bar{\text{x}}$ = (1 + 2 + 3 + 4 + 5) ÷ 5
= 15 ÷ 5
= 3

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Question 92 Marks

Find the median and mode of the data: $35,32,35,42,38,32,34$

Answer

Arranging the data in ascending order such that same numbers are put together, we get:
$32,32,34,35,35,38,42$
Here, $n =7$
Median $=$ value of $\frac{ n +1}{2}$ th observation $=$ value of the $4^{\text {th }}$ observation $=35$
Here, 32 and 35 , both occur twice. Therefore, 32 and 35 are the two modes.

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Question 102 Marks

If the heights of 5 persons are 140cm, 150cm, 152cm, 158cm and 161cm respectively, find the mean height.

Answer

The mean height = Sum of the heights ÷ Total number of persons
= (140 + 150 + 152 + 158 + 161) ÷ 5
= 761 ÷ 5
= 152.2cm.

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Question 112 Marks

Find the mean of x, x + 2, x + 4, x + 6, x + 8.

Answer

Mean = Sum of observations ÷ Number of observations
⇒ Mean = (x + x + 2 + x + 4 + x + 6 + x + 8) ÷ 5
⇒ Mean = (5x + 20) ÷ 5
⇒ Mean = 5(x + 4)5
⇒ Mean = x + 4

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Question 122 Marks

The enrolment of a school during six consecutive years was as follows:
1555, 1670, 1750, 2019, 2540, 2820
Find the mean enrollment of the school for this period.

Answer

The mean enrolment = Sum of the enrolments in each year ÷ Total number of years
The mean enrolment = (1555 + 1670 + 1750 + 2019 + 2540 + 2820) ÷ 6
= 12354 ÷ 6
= 2059.
Thus, the mean enrolment of the school for the given period is 2059.

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Question 132 Marks

Find the mean of first 10 even natural numbers.

Answer

The first 10 even natural numbers are 2, 4, 6, 8, 10, 12, 14, 16, 18 and 20.
Let $\bar{\text{x}}$ denote their arithmetic mean. Then,
$\bar{\text{x}}$ = (2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20) ÷ 10
= 110 ÷ 10
= 10

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