Note on Table, Pie chart and Graph

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Frequency Distribution Table

A frequency distribution table is one way you can organize data so that it make mare sense. By counting frequencies, we can make a frequency distribution table. Here are some test scores from a math class.

80 88 91 65 74 93 82 87 70 89

99 89 70 88 78 83 59 69 87 54

94 84 96 98 46 70 90 96 88 72

89 83 74 94 80 67 77 82 92 70

The above data can be organized into frequency distribution in several ways. One method is to use intervals as a basis. The smallest value in the above data is 46 and largest is 99. The interval from 46 to 99 is broken up into smaller subinterval (called class interval) for each class interval. For each class interval, the amount of data item falling in this interval is counted. The number is called the frequency of the class interval. The results are tabulated as frequency table as follows:

Class interval Tally Marks Frequency
40-50   1
50-60   3
60-70   5
70-80   8
80-90   13
90-100   9

Now, we can see the biggest number of the score are between 80 to 90 and the least number of scores between 40 and 50.

Pie charts

In pie-chart, the circle is divided into different sectors.It is a circular chart. Each sector represents an item in a data.

Reading pie-chart

The pie chart shows the result of a survey that was carried out to find out how student travels to school.

  • What is the most common food?
    The answer is the most common method of travel in the bus as this has the largest sector on the pie chart.

  • What fraction of people eats samosa?
    The answer is \(\frac{1}{3}\)

  • If 8 student eat samosa, how many students go to the hotel/canteen?
    The answer is 8÷\(\frac{1}{3}\)=24

Constructing pie-charts

To construct a pie chart you need to work out the fraction of the total that the sector represents. You can then convert this to an angle and draw the sector on the chart. Look at the following example.

The table below shows the grades achieved by 30 pupils in their final exams.

Grade A B C D E
Frequency 7 11 6 4

2

To show the information in a pie chart, take the following steps:

  1. Work out the total number of pupils 7 + 11 + 6 + 4 + 2=30
  2. To work out the angles of each sector, work out the fraction of the total that got each grade:
    A:\(\frac{7}{30}\), B:\(\frac{11}{30}\),C:\(\frac{6}{30}\), D:\(\frac{4}{30}\) and E:\(\frac{2}{30}\)
  3. There are 360° in the full turn, so to work out the angle, multiply the fraction by 360:
    Grade A:\(\frac{7}{30}\)\(\times\)360=84°
    Grade B:\(\frac{11}{30}\)\(\times\)360=132°
    Grade C:\(\frac{6}{30}\)\(\times\)360=72°
    Grade D:\(\frac{4}{30}\)\(\times\)360=48°
    Grade E:\(\frac{72}{30}\)\(\times\)360=24°
  4. Construct the pie chart as given:

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Graph

A line graph is most useful for displaying data or information.It is plotted as a series of points, which are then joined with the straight line.The end of line graph does not have to join to the axis.

How to make the line graph?

  • Use the data from the table to choose the appropriate scale. All scales start at 0.
  • Draw and label the scale on the vertical axis.
  • Draw and label the horizontal axis.
  • List the name of the each item.
  • Locate the point on the line segment.
  • Connect the points with line segments.

  • Pie charts differ from graphs because they do not feature a horizontal and vertical axis.
  • Pie charts are, however, a useful way of showing information.
  • Use a pencil, compass and ruler to draw pie chart, table and graph.
  • The graph is used to show the increase or decrease of the data.
  • The table is used to organize data.
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Very Short Questions

a) Upper-class limit of 30 - 35 is 35.

b) Lower- class limit of 10 - 15 is 10.

c) If the upper and lower limits of a class interval are 26 and 20 respectively, the class interval is 6.

d) If the lower and upper limits of a class interval are 5 and 10 respectively, the class interval is 5.

Solution:

Here, the given information, classes are presented in x- axis and Number of students are presented in y- axis.

Solution:

Total Number of Tickets sold = 2000

Then,

Tickets sold on first show (in degree)

= \(\frac{200}{2000}\)\(\times\) 360o

= 36o

Tickets sold on second show (in degree)

= \(\frac{500}{2000}\)\(\times\)360o

= 90o

Tickets sold on Third show (in degree)

= \(\frac{300}{2000}\)\(\times\)360o

= 54o

Tickets sold on fourth show (in degree)

= \(\frac{1000}{2000}\)\(\times\)360o

= 180o

Pie chart:-

Solution:

Given information,

Wages= 1500

Raw Material = 1200

Extras = 500

Fuel= 400

Total Expenditure = 3600

Now, Expenditure in Wages (in degree)

= \(\frac{1500}{3600}\)\(\times\)360o

= 150o

Expenditure on Raw Material (in degree)

= \(\frac{1200}{3600}\)\(\times\)360o

= 120o

Expenditure on Extras (in degree)

= \(\frac{500}{3600}\)\(\times\)360o

= 50o

Expenditure on Fuel (in degree)

= \(\frac{400}{3600}\)\(\times\)360o

= 40o

Showing in the pie- chart

Solution:

According to the question, Here's Cumulative frequency distribution table for the above set of data:

Class Frequency Scores less than Cumulative Frequency
0-10 3 10 3
10-20 8 20 3+8=11
20-30 8 30 11+8=19
30-40 6 40 19+6=25
40-50 5 50 25+5=30

This is less than Cumulative Frequency distribution.

Solution:

According to the question, Here's cumulative frequency distribution table for the above set of data.

Class Frequency Scores less than Cumulative Frequency
40-50 1 50 1
50-60 2 60 1+2=3
60-70 3 70 3+3=6
70-80 10 80 6+10=16
80-90 14 90 16+14=30
90-100 10 100 30+10=40

This is less than Cumulative frequency distribution.

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