NCERT Solutions for Class 7 Maths Chapter 3 Data Handling (EX 3.2) Exercise 3.2

Q.1 The scores in mathmatics test (out of 25) of 15 students is as follows:
19, 25, 23, 20, 9, 20, 15, 10, 5, 16, 25, 20, 24, 12, 20
Find the mode and median of this data, are they same?

Ans.

$\begin{array}{l}\text{Arranging the score in ascending order.}\\ \text{5,9,10,12,15,16,19,20,20,20,20,23,24,25,25}\\ \text{Since, mode is that value of observation which occurs for}\\ \text{the most number of time and median is the middle observation.}\\ \text{There are 15 values, so median would be the 8th observation}\\ \text{and 20 occurs 4 times.}\\ \text{So,}\boxed{\text{Mode}=\text{20\hspace{0.17em}and Median}=\text{20}}\\ \text{Yes both are same.}\end{array}$

Q.2

$\begin{array}{l}\text{The\hspace{0.33em}runs\hspace{0.33em}scored in a cricket match by 11 players is}\\ \text{as\hspace{0.33em}follows:}\\ \text{6,15,120,50,100,80,10,15,8,10,15}\\ \text{Find the mean, mode and median of this data.}\\ \text{Are the three same?}\end{array}$

Ans.

\begin{array}{l}\text{Arranging in ascending order to get}\\ \text{6,8,10,10,15,15,15,50,80,100,120}\\ \text{Mean}=\frac{6+8+10+10+15+15+15+50+80+100+120}{11}\\ =\frac{429}{11}=\boxed{39}\\ \text{Mode is that value of observation which occurs for the most}\\ \text{number of time and median is the middle observation}\text{.}\\ \text{There are 11 values, so median would be the 6th observation}\\ \text{and 15 occurs 3 times}\text{.}\\ \text{So,}\boxed{\text{Mode}=\text{15}\text{and Median}=\text{15}}\\ \text{No, these three are not same}\text{.}\end{array}

Q.3

$\begin{array}{l}\text{The\hspace{0.33em}weights\hspace{0.33em}}\left(\text{inkg.}\right)\text{of 15 students of a class are\hspace{0.33em}:}\\ \text{38,42,35,37,45,50,32,43,43,40,36,38,43,38,47}\\ \left(\text{i}\right)\text{Find the mode and median of this data.}\\ \left(\text{ii}\right)\text{Is there more than one mode?}\end{array}$

Ans.

\begin{array}{l}\text{Arranging the weight in ascending order}\text{.}\\ \text{32,35,36,37,38,38,38,40,42,43,43,43,45,47,50}\\ \text{Mode of given data is that value of observation which occurs for}\\ \text{the most number of time and median is the middle observation}\text{.}\\ \text{There are 15 values, so median would be the 8th observation}\\ \text{So, Median}=\boxed{\text{40}}\\ \text{Also 38 and 43 both occurs 3 times}\text{.}\\ \text{So,}\boxed{\text{Mode}=\text{38}\text{and 43}}\\ \text{Yes there are two mode for given data}\text{.}\end{array}

Q.4 Find the mode and median of the data:
13, 16, 12, 14, 19, 12, 14, 13, 14

Ans.

\begin{array}{l}\text{Arrange in ascending order to get:}\\ \text{12,12,13,13,14,14,1416,19}\\ \text{Mode of given data is that value of observation which occurs for}\\ \text{the most number of time and median is the middle observation}\text{.}\\ \text{There are 9 values, so median would be the 5th observation}\\ \text{So, Median}=\boxed{\text{14}}\\ \text{Also 14 occurs 3 times}\text{.}\\ \text{So,}\boxed{\text{Mode}=\text{14}}\end{array}

Q.5

\begin{array}{l}Tellwhetherthestatementistrueorfalse:\\ (i)Themodeisalwaysoneofthenumbersinadata.\\ \left(ii\right)Themeancanbeoneofthenumbersinadata.\\ \left(iii\right)Themedianisalwaysoneofthenumbersinadata.\\ \left(iv\right)Adataalwayshasamode.\\ \left(v\right)Thedata6,4,3,8,9,12,13,9hasmean9.\end{array}

Ans.

\begin{array}{l}\text{(i)}\boxed{\text{True}}\text{, because mode is the value that occurs most of}\\ \text{the time and it belongs to the given data}\text{.}\\ \text{(ii)}\boxed{\text{False}}\text{, Mean may or may not belong to the data}\text{.}\\ \text{(iii)}\boxed{\text{True}}\text{, because median is the middle observation}\\ \text{of given data}\text{.}\\ \text{(iv)}\boxed{\text{False}}\\ \text{The given data is: 6,4,3,8,9,12,13,9}\text{.}\\ \text{So, Mean}=\frac{6+4+3+8+9+12+13+9}{8}\\ =\frac{64}{8}\\ =8\end{array}