SChand CLASS 9 Chapter 14 Statistics, Introduction, Data and Frequency Distribution Exercise 14

 Exercise 14

Question 1

Ans: (i) The difference between the maximum and the minimum observation in a set of data is called the __range__ of the data 

(ii) The number of observation in a particular class interval is called the __frequency__ of the class interval

Question 2

(i) Lower limit of the class interval 26_33 is 26

(ii) The class mark of the class interval $20-29$ is $29.5$

(iii) Upper limit of the class interval $21-25$ is 25

(iv) The class mark of the close interval $9.5-19.5$ is $\frac{9.5+19.5}{2} \Rightarrow \frac{29}{2} \Rightarrow 14.5$

(v) If the class marks of a distribution are 32,39, 46, 53 then the width of each class interval is C.I = 39_32 =7

(vi) The mid point of a class interval is class its class mark 

(vii) If the class marks of  a distribution are 28, 34,46,52 then the class intervals of length C.I=34-28=6

(viii) If the class marks in a frequency distribution are $19.5,26.5,33.5,40.5,47.5,54,5,61.5$ then the class size of the distribution is clase size $\Rightarrow 26.5-19.5 \Rightarrow 7$

Question 3

Ans: (i) The range of the set of data 5,8, 15,21,7 10 is 10- 5=5

(ii) The range of the set of data 15, 13,14,17,19,16,14,15 is 19-14=5

(iii) The class mark of the class interval 10__19 is C.M of 9.5 -16.5 = $\frac{9.5+16.5}{2} \Rightarrow \frac{26}{2} \Rightarrow 13 .$

Question 4

Ans: We know that a variable which can assume any value between two given value is continuous  otherwise it is discrete 

Therefore.

(a) Size of Shoes - discrete

(b) number of pages in a book - continuous.

(c) distance  travelled by a train-continuous

(d) Time - continuous

$1.93-2.13$

similarly 

$2.13-2.33,2.33-2.53,2.53-2.73,2.73-2.93$,

$2.93-3.13$ and $9.13-2.33$

Question 5

Ans: The class mark are $2.03,2.23,2.43,2.63,2.83,3.03$ and $3.23$

Then class size $=$ difference of two consecutive class marks. $=2.23-2.03 \Rightarrow 0.20$

$\therefore$ class baundries will be

$\begin{aligned}& 2.03-\frac{0.20}{2} \\\Rightarrow & 2.03-0.10 \\\Rightarrow & 1.93\end{aligned}$$

$\text { and } \begin{aligned}& 2.03+\frac{0.20}{2} \\\Rightarrow & 2.03+0.10 \\\Rightarrow & 2.13\end{aligned}$

Question 6

Sol: Highest rent $\Rightarrow 84$

 Lowest rent $\Rightarrow 31$ 

$\therefore$ Range $\Rightarrow 84-31$

Taking class interval 40-50 (Excluding 50)

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(e) Daily temperature $\rightarrow$ continuous

(f) intelligence quotient. continuous

(g) Number of goals scored in discrete

(h) height - continuous

(i) weight - continuous

(j) number of room in apartment -discrete

(k) number of wage earners in a factory discrete.

(L) number of car. accidents - discrete.

Question 7

Sol: Greatest weight = 85 

 Lowest weight = 30

Range= 85-30=55

Taking class intervals such as 50-60 

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Question 8

Ans: Highest $P B=192$

Lowest $P B \Rightarrow 120$

Range $\Rightarrow 192-120 \Rightarrow 72$

Taking class intervals as 150-160(60 no included)

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Question 9

Ans: Hightest percentage $\Rightarrow 93$

Lowest percentage $\Rightarrow 03$

Range $\Rightarrow$ 93-03

$\Rightarrow 90$

Taking class Intervals as $40-49$

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Question 10

Ans: Highest plus rate $\Rightarrow 79$

Lowest. 11, 1, $\Rightarrow 51$

Range $=79-51$

$=28$

Using class Intervals 

like 51-55, 56-60

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