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Mathematics

Case Study

The following data gives the weights (in grams) of some marbles picked up randomly from 3 boxes. The data was presented in the tabular form as below:

Weight (in g)No. of Marbles
50-555
55-607
60-658
65-706
70-752
75-801
80-851

Based on the above information, answer the following questions:

  1. Class size of the given distribution is :
    (a) 5
    (b) 10
    (c) 50
    (d) 85

  2. Class mark of the 3rd class is :
    (a) 60
    (b) 65
    (c) 125
    (d) 62.5

  3. The number of marbles whose weight is more than or equal to 75 g is :
    (a) 0
    (b) 1
    (c) 2
    (d) 28

  4. The number of marbles whose weight is less than 70 g is :
    (a) 26
    (b) 28
    (c) 4
    (d) 2

  5. The class boundaries of the class 7th class interval are :
    (a) 80, 85
    (b) 80.5, 85.5
    (c) 79.5, 85.5
    (d) 80, 85.5

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Answer

1. Class size = Upper limit - lower limit

= 55 - 50

= 5.

Hence, option (a) is the correct option.

2. Class mark = Lower limit+Upper limit2\dfrac{\text{Lower limit} + \text{Upper limit}}{2}

= 60+652\dfrac{60 + 65}{2}

= 1252\dfrac{125}{2}

= 62.5

Hence, option (d) is the correct option.

3. Marbles weighing more than or equal to 75 g are

75-80 ⟶ 1

80-85 ⟶ 1

Total = 1 + 1 = 2

Hence, option (c) is the correct option.

4. Marbles weighing less than 70 g are

50-55 ⟶ 5

55-60 ⟶ 7

60-65 ⟶ 8

65-70 ⟶ 6

Total = 5 + 7 + 8 + 6 = 26

Hence, option (a) is the correct option.

5. Class interval of 7th class = 80 - 85

Hence, option (a) is the correct option.

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