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Q1. Given below are the heights ( in cm) of 11 boys of a class: 146, 143, 148, 132, 128, 139, 140, 152, 154, 142, 149. Arrange the above data in ascending order and find: (i) The height of the tallest boy. (ii) The height of the shortest boy. (iii) The range of the given data.

Solution

Arranging the given data, we get: 128, 132, 139, 140, 142, 143, 146, 148, 149, 152, 154 From the above data, we get: (i) The height of the tallest boy = 154 cm. (ii) The height of the shortest boy = 128 cm. (iii) Range of the given data = (154-128) cm = 26 cm.
Q2. Given below is the distribution of marks scored by some students in an examination: Marks 50-60 60-70 70-80 80-90 90-100 Number of students 10 9 6 3 2 (1)  What is the class size? (2)  What is the upper limit of the class interval 80-90? (3)  The results of how many students are recorded here?

Solution

(1)  Class size = Upper limit - Lower limit = 60 - 50 = 10 (2)  The upper limit of the class interval 80-90 is 90. (3)  Total number of students = 10 + 9 + 6 + 3 + 2 = 30       Thus, the results of 30 students are recorded.
Q3. A card is drawn at random from a well shuffled deck of playing cards. Find the probability that the card drawn is a red card.

Solution

Total space number space of space cards equals 52 Number space of space red space cards equals 26 therefore space Probability space of space drawing space straight a space red space card equals 26 over 52 equals 1 half
Q4. The following table shows various modes of transport used by 1500 students of a school. Mode of transport Bicycle Bus Walk Train Car Number of students 800 300 160 100 140   Draw a bar graph to represent the above data.

Solution

 
Q5. The number of children in 20 families of a locality are: 2, 2, 3, 1, 1, 2, 3, 2, 2, 1, 2, 2, 3, 1, 2, 1, 1, 3, 2, 2 State the frequency of each observation.

Solution

Arranging the data in ascending order, we get: 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3 We find that: 1 occurs 6 times 2 occurs 10 times 3 occurs 4 times Therefore, The frequency of families having 1 child is 6 The frequency of families having 2 children is 10 The frequency of families having 3 children is 4
Q6. The following table shows voting results of the colour preference of students. Colour Numbers Red 20 Blue 30 Green 40 Orange 50 Purple 60 Draw a pie chart showing above information.

Solution

For space red space colour comma space central space angle equals 20 over 200 cross times 360 degree equals 36 degree For space blue space colour comma space central space angle equals 30 over 200 cross times 360 degree equals 54 degree For space green space colour comma space central space angle equals 40 over 200 cross times 360 degree equals 72 degree For space orange space colour comma space central space angle equals 50 over 200 cross times 360 degree equals 90 degree For space purple space colour comma space central space angle equals 60 over 200 cross times 360 degree equals 108 degree
Q7. Marks obtained by a student in an examination are given below. Draw a pie diagram representing this information: Subjects English Hindi Science Mathematics Marks 100 95 82 83

Solution

  Subjects  Marks  Measure of the central angle English  100    Hindi  95    Science  82    Mathematics   83    Total 360 360    
Q8. The monthly income of a family is Rs. 15000. The monthly expenditure of the family on various items is given below. Items Education Rent Food Clothing Savings Expenditure (in Rs.) 2000 3500 6000 2500 1000 Represent the above data using a pie diagram.

Solution

  Items  Expenditure (in Rs.)  Measure of the central angle Education  2000    Rent  3500    Food  6000    Clothing  2500    Savings  1000    Total 15000 360   On the basis of the table, the pie diagram is as shown:  
Q9. Complete the following table: Classes 5-10 10-15 15-20 20-25 Class Marks   12.5      

Solution

Class space mark space for space class space 5 minus 10 equals fraction numerator 5 plus 10 over denominator 2 end fraction equals 15 over 2 equals 7.5 Class space mark space for space class space 15 minus 20 equals fraction numerator 15 plus 20 over denominator 2 end fraction equals 35 over 2 equals 17.5 Class space mark space for space class space 20 minus 25 equals fraction numerator 20 plus 25 over denominator 2 end fraction equals 45 over 2 equals 22.5 Thus, we have Classes 5-10 10-15 15-20 20-25 Class Marks  7.5 12.5  17.5  22.5
Q10. What is data and what is the need to organize data?

Solution

A collection of numerical facts regarding a particular type of information is called data. It is not easy to understand a raw data. To draw meaningful inferences and work upon it, we need to organize the data systematically.


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