In order to express raw data in the form of grouped data we use classes (or class intervals) for the values of the variables.

Depending upon the method of grouping data, class intervals can be divided into two categories.

(i) Overlapping Class Intervals: If the values of a variable in a collection of data are positive integers less than 50, we can group the data in five overlapping class intervals: 0 – 10, 10 – 20, 20 – 30, 30 – 40, 40 – 50. These are the groups of values of the variable. In case of overlapping intervals, 0 – 10 is the group containing the values of the variable that are greater than or equal to 0 but less than 10. Similarly, 10 – 20 is the group containing the values of the variable that are greater than or equal to 10 but less than 20.

(ii) Nonoverlapping Class Intervals: If the values of a variable in a collection of data are positive integers less than or equal to 50, we can group the data in five nonoverlapping intervals: 1 – 10, 11 – 20, 21 – 30, 31 – 40, 41 – 50. These are the groups of values of the variable. In case of nonoverlapping intervals, 1 – 10 is the group containing the values of the variable that are greater than or equal to 1 but less than or equal to10. Similarly, 11 – 20 is the group containing the values of the variable that are greater than or equal to 11 but less than or equal to 20.

**1.** The weights (in kg) of the teachers of s school are recorded as shown below.

60, 65, 63, 70, 65, 62, 65, 63, 64, 60, 68, 58, 62, 65, 63, 65, 64, 60, 62, 63.

If the collection of data be grouped into the class intervals 56 - 59, 59 - 62, 62 - 65, 65 - 68, 68 -71 then answer the following:

(i) What is the type of these class intervals?

(ii) Find the frequency of the class interval 59 - 62.

**Solution:**

(i) These are overlapping class intervals.

(ii) 3 (Since only 60, 60, 60 fall in this class).

**2.** The weights (in kg) of the teachers of s school are recorded as shown below.

60, 65, 63, 70, 65, 62, 65, 63, 64, 60, 68, 58, 62, 65, 63, 65, 64, 60, 62, 63.

If the collection of data be grouped into the class intervals 56 - 59, 60 - 63, 64 - 67, 68 - 71 then answer the following:

(i) What is the type of these class intervals?

(ii) Find the frequency of the class interval 59 - 62.

**Solution:**

(i) These are nooverlapping class intervals.

(ii) 7 (Since only 64, 64, 65, 65, 65, 65, 65 fall in this class).

**3.** The following are the marks obtained by 20 students of a class:

61, 62, 65, 65, 62, 70, 62, 70, 75, 72, 70, 60, 80, 85, 63, 85, 67, 80, 75, 65.

Prepare a frequency table by taking class intervals

(i) 60 - 65, 65 - 70, etc.

(ii) 60 - 65, 66 - 71, etc.

**Solution:**

**(i) **

**Class Interval**

**(Marks Obtained)**

**Tally Marks**

**Frequency**

65 – 70

////

4

70 – 75

////

4

75 – 80

//

2

80 - 85

//

2

85 - 90

//

2

**Total**

**20**

**(ii) **

**Class Interval**

**(Marks Obtained)**

**Tally Marks**

**Frequency**

66 – 71

////

4

72 – 77

///

3

78 – 83

//

2

84 - 89

//

2

**Total**

**20**

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