Excercise 3.2 Data Handling - NCERT Solutions Class 7

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Chapter 3 Ex.3.2 Question 1

The scores in mathematics test (out of $$25$$) of $$15$$ students are follows: -

=\left[ \begin{align} & \text{19, 25, 23, 20, 9, 20, 15, 10,} \\ & \,\,\,\,\,\text{ 5,16, 25, 20, 24, 12, 20}\text{.} \\ \end{align} \right]

Find the mode and median of the data. Are they same?

Solution

What is known?

Scores in mathematics test of $$15$$ students

What is unknown?

The mode and median of the data

Reasoning:

Mode – Mode of a given data is that value of observation which occurs for the most
number of times.
Median $$=$$ middle of observation (in this case, $$8$$th observation)

Steps:

Scores of $$15$$ students in mathematics test are =\left[ \begin{align} & \text{19, 25, 23, 20, 9, 20, 15, 10,} \\ & \,\,\,\,\,\text{ 5,16, 25, 20, 24, 12, 20}\text{.} \\ \end{align} \right]

Arranging scores in ascending order, we get

\left[ \begin{align} & \text{5, 9, 10, 12, 15, 16, 19, 20, } \\ & \,\,\text{20, 20, 20, 23, 24, 25, 25} \\ \end{align} \right]

Mode – Mode of a given data is that value of observation which occurs for the most

number of times.

Therefore$$, 20$$ occurs most of the time.

$$∴$$  Mode $$= 20.$$

Median $$=$$ middle of observation (in this case, $$8$$th observation)

$$∴$$ Median $$= 20$$

Yes, mode and median of the given observations are same.

Chapter 3 Ex.3.2 Question 2

The runs scored in a cricket match by $$11$$ players are as follows: -
$$6, 15, 120, 50, 100,80, 10,15,\\ 8, 10, 15$$

Find the mean, median and mode of the data. Are they same?

Solution

What is known?

Runs scored in a cricket match by $$11$$ Players

What is unknown?

The mean, median and mode of the data

Reasoning: \begin{align}\text{Mean}=\frac{\text{Sum of all scores}}{\text{Total no}\text{. of players}}\end{align}

Mode $$=$$ Mode is the observation that occurs highest number of times

Median$$=$$Median is the middle observation

Steps:

Total number of players $$= 11$$

Scores of players $$= 6, 15, 120, 50, 100,80, 10,15, 8, \\ \quad10, 15$$

\begin{align}{\rm{Mean}}& = \frac{{{\text{Sum of all scores}}}}{{{\text{Total no}}.{\text{of players}}}} \\ &= \frac{{\left[ \begin{array}{l}{\rm{6}} + {\rm{8}} + {\rm{1}}0 + {\rm{15}} + \\{\rm{15}} + {\rm{15}} + {\rm{5}}0 + {\rm{8}}0 + \\{\rm{1}}00 + {\rm{12}}0 \\\end{array} \right]}}{{11}} \\ &= \frac{{{\rm{429}}}}{{11}} \\ &= 39 \\\end{align}

Thus, mean $$= 39.$$

Arranging the scores into ascending order, we get
$$6, 8, 10,10, 15, 15,15, 50, 80, \\ 100, 120$$

Mode is the observation that occurs highest number of times

Here, $$15$$ occurs $$3$$ times

$$∴$$  Mode $$=15.$$

Median is the middle observation

$$∴$$  Median $$= 15$$ (6th observation)

Thus, Mean $$=$$ $$39$$ , Mode $$=$$ $$15$$ and median $$=$$ $$15$$

No, the mean, mode and median are not same.

Chapter 3 Ex.3.2 Question 3

The weights (in kg) of $$15$$ students of a class are: -

$$38, 42, 35, 37, 45, 50, 32, 43,43,\\ 40, 36, 38, 43, 38,47$$

(i) Find the median and mode of this data.

(ii) Is there more than one mode?

Solution

Reasoning:

What is known?

The weights (in kg) of $$15$$ students of a class

What is unknown?

The median and mode of this data.

Reasoning:

Mode $$=$$ Mode is the observation that occurs highest number of times

Median $$=$$ Median is the middle observation

Steps:

Total number of students $$=15$$

Weights of $$15$$ students $$= 38, 42, 35, 37, 45, 50, 32, 43,\\ \quad43, 40, 36,38, 43, 38, 47.$$

Arranging in ascending order, we get $$32, 35, 36, 37,38, 38,38, 40, 42, \\43, 43,43, 45, 47, 50$$

(i) Mode is the observation that occurred highest number of times.

Thus$$, 38$$ and $$43$$ occur highest number of times.

$$∴$$ Mode $$= 38$$ and $$43.$$

Also, median $$= 40$$ (8th observation)

(ii) Yes, there are two modes.

Chapter 3 Ex.3.2 Question 4

Find the mode and median of the data:$$13, 16, 12, 14, 19, 12, 14, 13, 14.$$

Solution

What is known?

Given numbers

What is unknown?

The mode and median of the data

Reasoning:

Mode $$=$$ Mode is the observation that occurs highest number of times

Median $$=$$ Median is the middle observation

Steps:

Given data $$= 13, 16, 12, 14, 19, 12, 14, 13, 14$$

Arranging the data in ascending order, we get $$12, 12, 13, 13, 14, 14, 14, 16, 19.$$

$$∴$$ Mode is the observation that occurs highest number of times.

$$∴$$ Mode $$= 14$$

Also, median is the middle observation.

$$∴$$ Median $$= 14$$ ($$5$$th observation)

Chapter 3 Ex.3.2 Question 5

Tell whether the statement is true or false:

(i) The mode is always one of the numbers in a data.

(ii) The mean is one of the numbers in a data.

(iii) The median is one of the numbers in a data.

(iv) The data $$6, 4, 3, 8, 9, 12, 13, 9,$$ has mean $$9.$$

Solution

Steps:

(i) True: Mode is the observations that occurs highest numbers of times. Therefore, it is one observation in a data.

(ii) False: Mean may or may not be one of the numbers in a data.

(iii) True: Median is the middle observations of the given data when it is arranged in ascending or descending order.

(iv) False: The given data $$6, 4, 3, 8, 9, 12, 13, 9.$$

\begin{align} \text{Mean} & =\frac{\left[ \begin{align} & 6+4+3+8+ \\& 9+12+13+9 \\\end{align} \right]}{8} \\ & =\frac{64}{8} \\ & =8 \\\end{align}

Therefore, mean is $$8.$$

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