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4. The marks obtained (out of 20) by 40 students of a class in a test are as follows

14, 16, 15, 11, 15, 14, 13, 16, 8, 10, 7, 11, 18, 15, 14, 19, 20, 7, 10, 17,
13, 12, 14, 15, 13, 16, 17, 14, 11, 10, 14, 13, 16, 8, 10, 7, 11, 18, 15, 20.
Make a frequency distribution table for the above data using class intervals of equal width in which
one class interval is 4-8 (excluding 8 and including 4).
5. A preliminary test was given to a group of 45 candidates for a job. The test was completed by the
candidates in the following time (in min.)

36, 31, 42, 26, 27, 44, 30, 42, 40, 26, 28, 49, 47, 46, 36, 37, 42, 40, 41, 32, 30, 49, 48, 33, 34, 35, 45,
44, 40, 42, 48, 27, 35, 41, 28, 30, 27, 44, 30, 42, 40, 32, 42, 48, 39

Prepare a grouped frequency table for this data taking 5 class intervals 25-30, 30-35, etc. and answer
the following questions.
( a) Which class interval has the highest frequency?

( b) Find the class mark of the class intervals having the least frequency.
( c) How many candidates completed the test in less than 40 minutes?
( d) How many candidates took 35 minutes or more to complete the test?
6. Find the class limits, if the class marks of grouped frequency distribution are as given below.
( a) 25, 35, 45, 55, 65 (b) 42, 50, 58, 66, 74

Graphical Representation of Data

The visual representation of data has major importance at the school level. Remember the old
words of wisdom, ‘A picture is worth a thousand words’. One of the most convincing and appealing
ways in which the data can be presented is through diagrams and graphs.

Data can be represented graphically in various ways:
1. Pictograph 2. Bar graph 3. Double bar graph 4. Histogram 5. Pie chart/circle graph
Before learning about a new type of graph or chart, let us recall what we already know.

Pictograph

A pictograph represents data in the form of pictures using symbols of objects or a part of objects.
In a pictograph, each complete picture or symbol represents a fixed number.
For example, the pictograph given below has been drawn using the symbol which represents
20 mm of rainfall.

Average Monthly Rainfall in May - August 2023

(Key: = 20 mm, = 10 mm)
Month Average Precipitation (in mm)
May

June

July

August

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