R.d Sharma 2022 Mcqs Solutions for Class 9 Maths Chapter 23 - Graphical Representation Of Statistical Data

Answer:

(d) Cumulative frequency distribution

We know that bar graph, histogram and frequency polygons are all graphical representation of statistical data.

Hence, the correct answer is option (d).

Answer:

(c) Cumulative frequency

In a frequency distribution, ogives are graphical representation of cumulative frequency.

Hence, the correct answer is option (c).

Answer:

(c) mid value of the class

Frequency polygon is the plot of frequencies vs. the mid values of the classes.

Hence, the correct answer is option (c)

Answer:

(c) frequency of the corresponding class interval

In a histogram the area of each rectangle is proportional to the frequency of the corresponding class interval.

Hence, the correct answer is option (c).

Answer:

(b) the upper limit of the concerned class interval

In the less than type of ogive the cumulative frequency is plotted against the upper limit of the concerned class interval.

Hence, the correct answer is option (b).

Answer:

(b) X-axis

In a histogram the class intervals or the groups are taken along the horizontal axis or X−axis.

Hence, the correct answer is option (b).

Answer:

(d) Horizontal axis and vertical axis

In a histogram the class intervals and frequencies are taken along horizontal and vertical axes respectively.

Hence, the correct option is (d).

Answer:

(b) class-intervals

In a histogram, the class rectangles are constructed with base as the class−intervals.

Hence, the correct answer is option (b).

Answer:

In the given frequency distribution,

Minimum class size = 5                 (10 − 5 = 5 or 15 − 10 = 5)

Class size of the class 25–45 = 45 − 25 = 20

Frequency of the class 25–45 = 8

We know

Adjusted frequency of a class = $\frac{\mathrm{Minimum} \mathrm{class} \mathrm{size}}{\mathrm{Class} \mathrm{size}}$ × Frequency of the class

∴ Adjusted frequency for the class 25–45 = $\frac{5}{20}\times 8$ = 2

Thus, in order to draw a histogram to represent the given frequency distribution the adjusted frequency for the class 25–45 is 2.

Hence, the correct answer is option (d).

Answer:

From the given bar graph, we have

The difference in the number of boys and girls in 2014 = (6 − 4.7) × 100 = 1.3 × 100 = 130

​The difference in the number of boys and girls in 2015 = 6.8 − 5.9) × 100 = 0.9 × 100 = 90

​​The difference in the number of boys and girls in 2016 = 7.6 − 6.9) × 100 = 0.7 × 100 = 70

​The difference in the number of girls and boys in 2017 = 9.7 − 8.3) × 100 = 1.4 × 100 = 140

Thus, in 2017 the difference between the number of boys and the number of girls was more.

Hence, the correct answer is option (d).
 

Answer:

In 2015 number of boys = 6.8
                              = 6.8 × 100
                              = 680 

Similarly,
In 2015 number of girls = 5.9
                              = 5.9 × 100 
                              = 590 
Total number of students in 2015 = Number of boys + Number of girls
= 680 + 590
= 1270

Therefore, total number of students in 2015 was 1270

Hence, the correct answer is option (b).

Answer:

The difference in the number of boys and girls in 2014 = (6 − 4.7) × 100 = 1.3 × 100 = 130

​The difference in the number of boys and girls in 2015 = 6.8 − 5.9) × 100 = 0.9 × 100 = 90

​​The difference in the number of boys and girls in 2016 = 7.6 − 6.9) × 100 = 0.7 × 100 = 70

​The difference in the number of girls and boys in 2017 = 9.7 − 8.3) × 100 = 1.4 × 100 = 140

Thus, in 2016 the difference between the number of boys and the number of girls was more.

Thus, the minimum difference between the number of boys and girls was in the year 2016, i.e., 70.

Hence, the correct answer is option (b).
 

Answer:

From the graph, we have
In 2017 the number of girls is more compared to the number of boys.

Hence, the correct answer is an option (d).

Answer:

We have
In 2016 number of boys = 7.6
                              = 7.6 × 100 
                              = 760

Also,
In 2016  number of girls = 6.9
                              = 6.9 × 100
                              = 690
Therefore, total number of students in 2016 was 1450
Similarly,
In 2017number of boys = 8.3
                              = 8.3 × 100
                              = 830

Also,
In 2017 number of girls = 9.7
                              = 9.7 × 100
                              = 970
Therefore, total  number of students in year 2017 was 1800.

Thus,  the ratio of the total sales in the year 2016 and that in 2017 = 1450 : 1800
                                                                                                          = 29 : 36

Hence, the correct answer is option (c).
 

Answer:

(i) From the given bar graph, we have

The difference in the number of drinks in companies A and B in 2015 = 6 − 4.7 = 1.3

The difference in the number of drinks in companies A and B in 2016 = 6.8 − 5.9 = 0.9

The difference in the number of drinks in companies A and B in 2017 = 7.6 − 6.9 = 0.7

The difference in the number of drinks in companies A and B in 2018 = 9.7 − 8.3 = 1.4

Thus, in 2018 the difference in the number of drinks in companies A and B was more.

Hence, the correct answer is an option (a).

(ii) We have
In 2016 sales of A = 6.8
                              = 6.8 × 10,000 units
                              = 68000 units

Similarly,
In 2016 sales of B = 5.9
                              = 5.9 × 10,000 units
                              = 59000 units
Therefore, total sales of A and B in the year 2016 were 127,000.

Disclaimer: In this question the option should be 116,000, 127,000, 138,000 and 149,000.

Hence, the correct answer is option (b).

(iii) We have,
The minimum difference between the sales of company A and B was in year 2017 and it is 0.7
= 0.7 × 10,000
= 70,000

Hence, the correct answer is option (b).

(iv) In 2018,  the sales of company B more than the sales of company A.

Hence, the correct answers option (d).

(v) We have
In 2017 sales of A = 7.6
                              = 7.6 × 10,000 units
                              = 76000 units

Also,
In 2017 sales of B = 6.9
                              = 6.9 × 10,000 units
                              = 69000 units
Therefore, total sales of A and B in the year 2017 was 145,000.
Similarly,
In 2018 sales of A = 8.3
                              = 8.3 × 10,000 units
                              = 83000 units

Also,
In 2017 sales of B = 9.7
                              = 9.7 × 10,000 units
                              = 97000 units
Therefore, total sales of A and B in the year 2017 was 180,000.

Thus,  the ratio of the total sales in the year 2017 and that in 2018 = 145,000 : 180,000
                                                                                                          = 29 : 36

Hence, the correct answer is option (b).

Answer:

(i) From the given bar graph, we have

The difference in the sales of cars and Scooters in 2015 = 6.6 − 5.7 = 0.9

The difference in the sales of cars and Scooters in 2016 = 7.3 − 6.5 = 0.8

The difference in the sales of cars and Scooters in 2017 = 8.1 − 6.6 = 1.5

The difference in the sales of cars and Scooters in 2018 = 10 − 8.2 = 1.8

Thus, in 2016 The difference in the sales of cars and Scooters was least

Hence, the correct answer is an option (b).

(ii) We have
In 2015 sales of scooters = 6.6
                              = 6.6 × 1000 units
                              = 6600 units

Also
In 2015 sales of cars = 5.7
                              = 5.7 × 1000 units
                              = 5700 units
Therefore, the total sales of scooters and cars in the year 2015 were 12,300.
Similarly,
In 2016 sales of scooters = 7.3
                              = 7.3 × 1000 units
                              = 7300 units

Also
In 2016 sales of cars = 6.5
                              = 6.5 × 1000 units
                              = 6500 units
Therefore, the total sales of scooters and cars in the year 2016 were 13,800.

Thus, the total number of vehicles sold in the years 2015 and 2016 was 26,100.

Hence, the correct answer is option (a).

(iii) We have,
The maximum difference between the sales of scooters and cars was in the year 2018 and it is 1.8
= 1.8 × 1000
= 1800

Hence, the correct answer is option (c).

(iv) We have,
Scooters sold in the year 2015 = 6.6 × 1000 = 6600
Scooters sold in the year 2016 = 7.3 × 1000 = 7300
​Scooters sold in the year 2017 = 8.1 × 1000 = 8100
​Scooters sold in the year 2018 = 10 × 1000 = 10,000

Thus, total scooters sold in the 4 years = 6600 + 7300 + 8100 + 10,000
                                                              = 32,000
 
Hence, the correct answer is option (d).


(v) We have
In 2016 sales of scooters = 7.3
                              = 7.3 × 1000 units
                              = 7300 units

Also
In 2016 sales of cars = 6.5
                              = 6.5 × 1000 units
                              = 6500 units
Therefore, the total sales of scooters and cars in the year 2016 was 13,800.

In 2018 sales of scooters = 10
                              = 10 × 1000 units
                              = 10000 units

Also
In 2018 sales of cars = 8.2
                              = 8.2 × 1000 units
                              = 8200 units
Therefore, the total sales of scooters and cars in the year 2018 was 18,200.
Thus,  the ratio of the total sales in the year 2016 and that in 2018 = 13,800: 18,200
                                                                                                          = 69 : 91

Hence, the correct answer is option (b).

Answer:

Statement-1:
In a histogram, the horizontal axis represents the class intervals whose width is fixed and the varying data is plotted along the $y-axis$. So in all the rectangles of a histogram, the width remains the same, and the length changes.

So the correct statement is "In the histogram, the area of each rectangle is proportional to the frequency of its class.

Statement-2:

Answer:

Statement-1: False
Because in a histogram, the horizontal axis represents the class intervals whose width is fixed, and varying data is plotted along the y-axis. So, in all rectangles of a histogram, the width remains the same, and the length changes.

Statement-2: True
$\mathrm{Adjusted} \mathrm{frequency} \mathrm{of} \mathrm{a} \mathrm{class} = \frac{\mathrm{Minimum} \mathrm{class} \mathrm{size}}{\mathrm{Class} \mathrm{size}} \times \mathrm{Frequency} \mathrm{of} \mathrm{the} \mathrm{class}$

Hence, the correct answer is option (d).

Answer:

Statement-1 True
Because when mid-points or class marks are given it is assumed that the frequency corresponding to the class mark a is spread over the interval $a-\frac{h}{2} \mathrm{to} a+\frac{h}{2}$, where h is the jump from one value to the other.

Statement-2 False,
The difference between two consecutive class marks is always equal to the class size.
Now, class size = $1.14-1.04=0.1$
But in the class intervals, 1.55 - 1.73,
class size = $1.73-1.55=0.8$ which is not equal to the class size found previously.

Hence, the correct answer is option (c).