1. Since, Histogram is a graphical representation of data, if data represented in manner of class-interval.
Therefore, for case (b) and (d), we would be use a histogram to show the data, because in these cases, data can be divided into class-intervals.
In case (b), a group of competitions having different heights in an athletics meet.
In case (d), the number of passengers boarding trains in an interval of one hour at a station.
2. The frequency distribution table is as follows:
The illustration of data by bar-graph is as follows:
3. The representation of data by frequency distribution table using tally marks is as follows:
4. (i) 830 – 840 group has the maximum number of workers.
(ii) 10 workers can earn more than ` 850.
(iii) 20 workers earn less than ` 850.
5. (i) The maximum number of students watched T.V. foe 4 – 5 hours.
(ii) 34 students watched T.V. for less than 4 hours.
(iii) 14 students spent more than 5 hours in watching T.V.
6. (i) 10% represents 100 people.
Hence, 200 people were surveyed.
(ii) light music is liked by the maximum number of people.
7. (i) Winter season got the most votes.
8. Here central angle = 360° and total number of people = 36
(i) The student scored 105 marks in Hindi.
(ii) Marks obtained in Mathematics = 135
Marks obtained in Hindi = 105
Difference = 135 – 105 = 30
Thus, 30 more marks were obtained by the student in Mathematics than in Hindi.
(iii) The sum of marks Social Science and Mathematics = 97.5 + 135 = 232.5
The sum of marks in Science and Hindi = 120 + 105 = 225
Yes, the sum of the marks in Social Science and Mathematics is more than that in Science and Hindi.
Pie chart at above given data is as follows
11. (a) There are four letters A, B, C and D in a spinning wheel. So there are 4 outcomes.
(b) When two coins are tossed together. There are four possible outcomes HH, HT, TH, TT.
(Here HT means head on first coin and tail on second coin and so on.)
12. (i) (a) Outcomes of event of getting a prime number are 2, 3, and 5.
(b) Outcomes of event of not getting a prime number are 1, 4 and 6.
(ii) (a) Outcomes of event of getting a number greater than 5 is 6.
(b) Outcomes of event of not getting a number greater than 5 are 1, 2, 3, 4 and 5.
13. (a) In a spinning wheel, there are five pointers A, A, B, C, D. So there are five outcomes. Pointer stops at D which is one outcome.
(b) There are 4 aces in a deck of 52 playing cards. So, there are four events of getting an ace.
(c) Total number of apples = 7
Number of red apples = 4
14. (i) Outcome of getting a number 6 from ten separate slips is one.
(ii) Numbers less than 6 are 1, 2, 3, 4 and 5 which are five. So there are 5 outcomes.
(iii) Number greater than 6 out of ten that are 7, 8, 9, 10. So there are 4 possible outcomes.
(iv) One digit numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9 out of ten.
There is one blue sector out of five sectors.
Non-blue sectors = 5 – 1 = 4 sectors
16. When a die is thrown, there are total six outcomes, i.e., 1, 2, 3, 4, 5 and 6.
(i) (a) 2, 3, 5 are prime numbers. So there are 3 outcomes out of 6.
(b) 1, 4, 6 are not the prime numbers. So there are 3 outcomes out of 6.
(ii) (a) Only 6 is greater than 5. So there is one outcome out of 6.
(b) Numbers not greater than 5 are 1, 2, 3, 4 and 5. So there are 5 outcomes out of 6.