The marks scored by 40 candidates in an examination (out of 100) is given below:

75, 65, 57, 50, 32, 54, 75, 67, 75, 88, 80, 42, 40, 41, 34, 78, 43,

61, 42, 46, 68, 52, 43, 49, 59, 49, 67, 34, 33, 87, 97, 47, 46, 54,

48, 45, 51, 47, 41, 43.

Prepare a frequency distribution table with the class size 10.

Take the class intervals as (30-39), (40-49), ... and answer the following questions:

(i) Which class intervals have highest and lowest frequency?

(ii) Write the upper and lower limits of the class interval 30-39

(iii) What is the range of the given distribution?

Theory.

The number of times a particular observation occurs in data is called frequency.

Showing data in tabular form with showing frequency of each distribution. This representation is called Frequency distribution table.

(i) As looking in Frequency distribution table

Highest Frequency is 16

And the group of marks having highest frequency is 40-49

∴ Maximum number of students have got marks between 40 to 49.

Lowest Frequency is 1

And the group of marks having lowest frequency is 90-99

∴ Minimum number of students have got marks between 90 to 99.

(ii) The given distribution is in inclusive form . It should be converted in exclusive form

Upper limit of 1^st interval is 39

Lower limit of 2^nd interval is 40

= = = 0.5

Actual upper limit = Stated upper limit + = 39 + 0.5 = 39.5

Actual lower limit = Stated lower limit – = 30 – 0.5 = 29.5

∴ Upper limit of group 30-39 is 29.5

Lower limit is lower most value of group

∴ Lower limit of group 30-39 is 30.5

(iii) Range = highest – lowest

Highest marks in class is 97

Lowest marks in class is 32

Range = 97 – 32 = 65