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Page No 219:
Question 1:
Which one of the following is not the graphical representation of statistical data:
(a) Bar graph
(b) Histogram
(c) Frequency polygon
(d) Cumulative frequency distribution
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).
Page No 219:
Question 2:
In a frequency distribution, ogives are graphical representation of
(a) Frequency
(b) Relative frequency
(c) Cumulative frequency
(d) Raw data
Answer:
(c) Cumulative frequency
In a frequency distribution, ogives are graphical representation of cumulative frequency.
Hence, the correct answer is option (c).
Page No 219:
Question 3:
A frequency polygon is constructed by plotting frequency of the class interval and the
(a) upper limit of the class
(b) lower limit of the class
(c) mid value of the class
(d) any values of the class
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)
Page No 219:
Question 4:
In a histogram the area of each rectangle is proportional to
(a) the class mark of the corresponding class interval
(b) the class size of the corresponding class interval
(c) frequency of the corresponding class interval
(d) cumulative frequency of the corresponding class interval
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).
Page No 219:
Question 5:
In the 'less than' type of ogive the cumulative frequency is plotted against
(a) the lower limit of the concerned class interval
(b) the upper limit of the concerned class interval
(c) the mid-value of the concerned class interval
(d) any value of the concerned class interval
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).
Page No 219:
Question 6:
In a histogram the class intervals or the group are taken along
(a) Y-axis
(b) X-axis
(c) both of X-axis and Y-axis
(d) in between X and Y axis
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).
Page No 219:
Question 7:
A histogram is a pictorial representation of the grouped data in which class intervals and frequency are respectively taken along
(a) vertical axis and horizontal axis
(b) vertical axis only
(c) horizontal axis only
(d) Horizontal axis and vertical axis
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).
Page No 219:
Question 8:
In a histogram, each class rectangle is constructed with base as
(a) frequency
(b) class-intervals
(c) range
(d) size of the class
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).
Page No 219:
Question 9:
Consider the following frequency distribution:
Class interval : | 5 – 10 | 10 – 15 | 15 – 25 | 25 – 45 | 45 – 75 |
Frequency : | 6 | 12 | 10 | 8 | 15 |
To draw a histogram to represent the above frequency distribution the adjusted frequency for the class 25-45 is
(a) 6
(b) 5
(c) 3
(d) 2
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 = × Frequency of the class
∴ Adjusted frequency for the class 25–45 = = 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).
Page No 219:
Question 10:
In the given figure, shows the bar graph of the number of boys and number of girls in a school from 2014 to 2017.
In which year was the difference between the number of boys and the number of girls was more?
(a) 2014
(b) 2015
(c) 2016
(d) 2017
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
âThe difference in the number of boys and girls in 2015 = 6.8 − 5.9) × 100 = 0.9 × 100 = 90
ââThe difference in the number of boys and girls in 2016 = 7.6 − 6.9) × 100 = 0.7 × 100 = 70
âThe 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).
Page No 220:
Question 11:
In the given figure, total number of students in the year 2015 was
(a) 1160
(b) 1270
(c) 1380
(d) 1490
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).
Page No 220:
Question 12:
In the given figure, the minimum difference between the number of boys and girls in any year in the given period was
(a) 90
(b) 70
(c) 50
(a) 30
Answer:
The difference in the number of boys and girls in 2014 = (6 − 4.7) × 100 = 1.3 × 100 = 130
âThe difference in the number of boys and girls in 2015 = 6.8 − 5.9) × 100 = 0.9 × 100 = 90
ââThe difference in the number of boys and girls in 2016 = 7.6 − 6.9) × 100 = 0.7 × 100 = 70
âThe 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).
Page No 220:
Question 13:
In the given figure, in which year the number of girls was more than the number of boys?
(a) 2014
(b) 2015
(c) 2016
(d) 2017
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).
Page No 220:
Question 14:
In the given figure, the ratio between the number of students in the year 2016 and 2017 was
(a) 107 : 145
(b) 127 : 145
(c) 29 : 36
(d) 107 : 127
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).
Page No 220:
Question 15:
Following bar graph represents the sales of cold drinks of two companies A and B from 2015 to 2018.
Bar graph represents the sales of cold drinks of two companies A and B from 2015 to 2018
Read the above bar graph and answer the following questions:
(i) The year in which the difference between the sales of two companies was highest, was
(b) 2015
(c) 2016
(d) 2017
(ii) Total sales of A and B in the year 2016 was
(b) 1,270,000 units
(c) 1,380,000 units
(d) 1,490,000 units
(iii) The minimum difference between the sales of company A and B in any year in the given period was
(b) 70,000 units
(c) 50,000 units
(d) 30,000 units
(iv) In which year was the sales of company B more than the sales of company A?
(b) 2016
(c) 2017
(d) 2018
(v) The ratio of the total sales in the year 2017 and that in 2018 was
(b) 29 : 36
(c) 127 : 145
(d) 107 : 127
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).
Page No 221:
Question 16:
Read the following bar graph and answer the following questions:
(i) In which year was the difference between the sales of the scooters and the sales of cars the least?
(b) 2016
(c) 2017
(d) 2018
(ii) Total number of vehicles (scooters and cars) sold in the year 2015 and 2016 was
(b) 28,500
(c) 25,100
(d) 27,500
(iii) The maximum difference between the sales of scooters and cars, in any year, in the given period was
(b) 1700
(c) 1800
(d) 2000
(iv) The total number of scooters sold in the four years was
(b) 27,000
(c) 31,000
(d) 32,000
(v) The ratio between the total number of vehicles sold (scooters and cars) in the year 2016 and that in the year 2018.
(b) 69 : 91
(c) 147 : 182
(d) 46 : 49
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
âScooters sold in the year 2017 = 8.1 × 1000 = 8100
âScooters 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).
Page No 221:
Question 17:
âEach of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. Mark the correct choice.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) âStatement-1 is false, Statement-2 is true.
Statement-1 (Assertion): In a histogram, the areas of each rectangle is proportional to the frequencies of its classes.
Statement-2 (Reason): In a histogram, the lengths or heights of rectangles are proportional to the frequencies.
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 . 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:
Hence, the correct answer is option (a).
Page No 221:
Question 18:
âEach of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has the following four choices (a), (b), (c), and (d), only one of which is the correct answer. Mark the correct choice.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) âStatement-1 is false, Statement-2 is true.
Statement-1 (Assertion): In a histogram, the area of each rectangle is proportional to the class size of the corresponding interval.
Statement-2 (Reason): To draw the histogram of a continuous frequency distribution with unequal class intervals, the frequencies of classes are adjusted by using the formula:
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
Hence, the correct answer is option (d).
Page No 222:
Question 19:
âEach of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. Mark the correct choice.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) âStatement-1 is false, Statement-2 is true.
Statement-1 (Assertion): To draw the histogram of a continuous frequency distribution when class marks of class intervals are given, it is assumed that the frequency corresponding to the class mark a is spread over the interval , where h is the jump from one value to the other.
Statement-2 (Reason): The class marks of a continuous frequency distribution are: 1.04, 1.14, 1.24, 1.34, 1.44, 1.54, 1.64, then the last interval is 1.55 - 1.73.
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 , 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 =
But in the class intervals, 1.55 - 1.73,
class size = which is not equal to the class size found previously.
Hence, the correct answer is option (c).
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