Statistics -Data Representation (Bar Chart And Pie Charts) JSS2 Mathematics Lesson Note

 STATISTICS – DATA PRESENTATION

FREQUENCY TABLE

EXAMPLE 1: The following figures show the number of children per family in a sample of 40 households. 1, 2, 4, 3, 5, 3, 8, 3, 2, 3, 4, 5, 6, 5, 4, 2, 1, 3, 2, 4, 5, 3, 8, 7, 6, 5, 4, 5, 7, 6, 3, 8, 6, 3, 5, 7, 5, 4, 3.

a. Use a tally mark to prepare a frequency table for the data

b. What is the highest frequency of the number of children per family?

Solution

Example 2: In a further mathematics test the following marks were obtained by a group of students 85, 75, 95, 80, 75, 80, 90, 84, 95, 84, 85, 80, 80, 75, 80, 75, 80, 84, 81, 80, 75, 90, 80.

Use a tally mark to prepare a frequency table for this data.

Solution:

NUMBER      TALLY             FREQUENCY 

75                 ////                 5

80                   ////                    9

81                    /                      1

84                     ///                    3

85                   //                     2

90                  ///                    3

95                   //                         2

a. How many students took part in the test? 25 students

b. Which mark had the highest frequency? 80 marks

AVERAGE, MEAN MEDIAN  AND MODE

Average is a single value used to represent a set of numbers (i.e all values in as et data)

The most commonly used statistic is average.

MEDIAN = THE NUMBER IN THE MIDDLE AFTER THE ARRANGEMENT OF THE DATA.

MODE IS THE VALUE THAT OCCURS MOST FREQUENTLY.

EXAMPLES: Calculate the mean, median, and mode of the following data

a. 45, 50, 55, 54, 48, 53, 50, 55

b. 38, 35, 36, 30.8, 34.7, 37.9, 33.1

c. 3, 0,4,7, 0, 5, 3, 4, 0, 3, 6, 5, 5,4, 6, 5

Solution:

Mean = 45+50+ 55+ 54+ 48+ 53+ 50+ 55

                                                 8

= 410/8

= 51.25

Median = 45, 48, 50, 50, 53, 54, 55,55

50 + 53

  2

= 52

Mode = 50 and 55 

Average

The average or mean of a set of numbers is defined by the formula:

Example 

Bar Charts

A Bar chart is a series of rectangular bars of the same width, drawn vertically or horizontally, with an equal space between them, with the height of each bar being a depiction of the data it is representing.

Example

The table below lists several models of Blackberry cellular phones and the amount of each that an electronic store has in stock. Draw a vertical and horizontal bar chart to represent the data.

Pie Charts

A Pie chart is a circular diagram divided into sectors, with the size of each sector representing the magnitude of data it is depicting. Each sector of a pie chart can either be displayed in percentages (note all sectors must add up to 100%) or as an angle (note all sectors must add up to 360o).

Example

The table below lists some of the most popular football clubs and the number of students at a given institution that supports each. Use a Pie chart to represent the information given in the table.

The Pie Chart above depicts each sector as percentages. To calculate the percentages for each sector use the formula below:

% of a sector      =        Number of students                       x              100

                                       Total number of students

So, to calculate the percentage of Chelsea fans:

% of Chelsea fans            =             50           x              100

                                                                      990

% of Chelsea fans            =             5%

For Pie charts that depict each sector as angles, the angles for each sector are found using the formula below:

The angle of a sector              =       Number of students                       x              360

                                                     Total number of students                           

So, to calculate the angle of the Chelsea sector:

Angle of Chelsea sector                =             50           x              360

                                                                        990

Angle of Chelsea sector                                =             18 de

Note:    In most cases, the questions set on Pie charts require those drawn depicting sectors in percentages.

Line Graphs

Line graphs are mostly used in depicting trends, and as such, values are in most cases plotted against time. A line graph is drawn by connecting a line to consecutive values, with a circle/point made at each value being depicted.

Example

The table below lists the amount of Toyota motor vehicles produced in April over the period 2000- 2010.

Year Number of Toyota Motor Vehicles Produced

2000 220,382

2001 260,879

2002 213,546

2003 238,890

2004 227,678

2005 245,376

2006 240,224

2007 224,100

2008 258,100

2009 248,024

2010 249,123