2 Marks Questions

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, $\mathrm{n}=7$
Median $=$ value of $\frac{\mathrm{n}+1}{2}$ 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 $140\ cm, 150\ cm, 152\ cm, 158\ cm$ and $161\ cm$ respectively, find the mean height.

Answer

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

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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
$\Rightarrow $ Mean $= (x + x + 2 + x + 4 + x + 6 + x + 8) ÷ 5$
$\Rightarrow $ Mean $= (5x + 20) ÷ 5$
$\Rightarrow $ Mean $= 5(x + 4)5$
$\Rightarrow $ 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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Question 142 Marks

Find the mode of the data: 12, 14, 16, 12, 14, 14, 16, 14, 10, 14, 18, 14

Answer

Mode = 14

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Question 152 Marks

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

Answer

2, 3 and 4 are three modes.

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Question 162 Marks