**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.

Therefore 20% represents 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.

(ii) Central angle of summer season =

Central angle of winter season

**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.

So the probability of the pointer stopping on D =

(b) There are 4 aces in a deck of 52 playing cards. So, there are four events of getting an ace.

So, probability of getting an ace

(c) Total number of apples = 7

Number of red apples = 4

Probability of getting red apple

**14.** (i) Outcome of getting a number 6 from ten separate slips is one.

Therefore, probability of getting a number

(ii) Numbers less than 6 are 1, 2, 3, 4 and 5 which are five. So there are 5 outcomes.

Therefore, probability of getting a number less than

(iii) Number greater than 6 out of ten that are 7, 8, 9, 10. So there are 4 possible outcomes.

Therefore, probability of getting a number greater than

(iv) One digit numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9 out of ten.

Therefore, probability of getting a 1-digit number

**15. **There are five sectors. Three sectors are green out of five sectors. Therefore, probability of getting a green sector =

There is one blue sector out of five sectors.

Non-blue sectors = 5 – 1 = 4 sectors

Therefore, probability of getting a non-blue sector

**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.

Therefore, probability of getting a prime number

(b) 1, 4, 6 are not the prime numbers. So there are 3 outcomes out of 6.

Therefore, probability of getting a prime number

(ii) (a) Only 6 is greater than 5. So there is one outcome out of 6.

Therefore, probability of getting a number greater than

(b) Numbers not greater than 5 are 1, 2, 3, 4 and 5. So there are 5 outcomes out of 6.

Therefore, probability of not getting a number greater than