Frequency Distribution — Case-Study Based Questions

Case Study

To maintain the health report card in a hospital, the weights of new born babies are recorded on regular basis.

During a week, the weights (in kg) of new born were recorded as below :

2.7, 2.6, 3.1, 2.2, 2.4, 2.9, 3.0, 2.5, 2.8, 2.5, 2.8, 2.9, 2.2, 2.9, 2.7, 2.8, 2.3, 2.8, 2.1, 2.2

Based on the above information, answer the following questions:

1. Range of the data is :
   (a) 1 kg
   (b) 0.4 kg
   (c) 0.5 kg
   (d) 1.1 kg

2. How many babies are born during the week?
   (a) 10
   (b) 16
   (c) 17
   (d) 20

3. How many babies weigh less than 2.4 kg?
   (a) 7
   (b) 6
   (c) 5
   (d) 4

4. How many babies weigh more than 2.7 kg?
   (a) 10
   (b) 9
   (c) 8
   (d) 7

5. How many babies weigh 2.8 kg?
   (a) 4
   (b) 5
   (c) 6
   (d) 3

Answer

1. Range = Highest value - Lowest value

= 3.1 - 2.1

= 1 kg

Hence, option (a) is the correct option.

2. Total babies born during the week = 20

Hence, option (d) is the correct option.

3. Babies weighing less than 2.4 kg are

2.2, 2.2, 2.3, 2.1, 2.2

Total = 5

Hence, option (c) is the correct option.

4. Babies weighing more than 2.7 kg are

2.8, 2.9, 3.0, 2.8, 2.9, 2.9, 2.8, 2.8, 3.1

Total = 9

Hence, option (b) is the correct option.

5. From data,

Babies weighing 2.8 kg = 4.

Hence, option (a) is the correct answer

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:

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

Answer

1. Class size = Upper limit - lower limit

= 55 - 50

= 5.

Hence, option (a) is the correct option.

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

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

= $\dfrac{125}{2}$

= 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.