Statistical graphs – Pie Graph

Introduction

The purpose of graph in statistics is to convey the data to the viewers into pictorial form. That is after you have organized the data into a frequency distribution, you need to present them in graphical form. The reason is that it is easier for most people to understand the meaning of data presented graphically than data presented numerically in frequency distributions or tables. This is especially true if users have little or no statistical knowledge.

Uses of statistical graphs

1.      Statistical graphs can be used to analyse a data or described it.

2.       They are used to get the audience’s attention in a speaking presentation.

3.      They are also used to discover a pattern in a situation over a period of time.

4.      Statistical graphs are used to summarize a data.

The Pie chart or Graph:

This is a graph divided into sectors, each sector representing a different value of category. We note that, the angle of each sector is proportional to the value of the part of the data it represents. Pie graphs are used extensively in statistics. The purpose of the pie graph is to show the relationship of the whole by visually comparing the sizes of the sections. Percentages or proportions can be used. The variable is normal or categorical.

Definition: A pie graph is a circle that is divided into sections or wedges according to the percentage of frequencies in each category of the distribution.

The example below shows the procedure for constructing a pie graph.

Example one:

The table below shows the number of students who offer certain subjects.

SUBJECT	NO. OF STUDENTS
Mathematics	45
Physics	39
Chemistry	28
Biology	14
Economics	36
History	18

a)      Draw a pie graph to illustrate the above information.

b)      What percentages of the number of students offer mathematics?

SOLUTION

STEPS:

Step 1. Since there are 360⁰ in a circle, the frequency for each class must be converted into a proportional part of the circle. The conversion is done by using the formula;

where f = frequency for each class and n = sum of frequencies. Hence the following conversions are obtained. The degrees should sum up to 360⁰.

Step 2. Each frequency must be converted to a percentage. This is done by using the formula:

 Hence, the following percentages are obtained. The percentages should sum up to 100%.

Step 3. Next, using a protractor and a compass, draw the graph using the appropriate degree measures found in step 1, and label each section with the name and percentages, as shown below:

a.       From the table in step 2, the percentage of students who offered mathematics is 25%.

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Statistical graphs – Bar Graph or Chart

Introduction

Having organized the data into a frequency distribution, you need to present them in graphical form. The purpose of graph in statistics is to convey the data to the viewers into pictorial form. The reason is that it is easier for most people to understand the meaning of data presented graphically than data presented numerically in frequency distributions or tables. This is especially true if users have little or no statistical knowledge.

Uses of statistical graphs

1.      Statistical graphs can be used to analyse a data or described it.

2.       They are used to get the audience’s attention in a speaking presentation.

3.      They are also used to discover a pattern in a situation over a period of time.

4.      Statistical graphs are used to summarize a data.

Bar Graphs:

When the data are qualitative or categorical, bar graphs can be used to represent the data. It is a diagram consisting of a series of horizontal or vertical bars of equal width. We note that the length or height of each bar is equal to the frequency it represents and the bars are equally spaced.

Definition: A bar graph represents the data by using vertical or horizontal bars whose heights or lengths represent the frequencies of the data.

NOTE:

Bar graph may be represented VERTICALLY OR HORIZONTALLY.

Ø  Vertically Representation; the class interval is plotted on the horizontal axis and the frequency on the vertical axis as the diagram below:

Ø  Horizontal Representation; the class interval is plotted on the vertical axis and the frequency on the horizontal axis as the diagram below:

The example below shows the procedure for constructing a bar graph.

Example one:

The following table shows the interval of a rainfall pattern in a certain town.

Year	1991	1992	1993	1994	1995	1996
Rainfall	30.5	43.0	66.0	58.0	49.5	31.0

1.      Draw a bar graph for the data.

2.      Determine the modal rainfall year.

SOLUTION

Steps:

A.    Draw and label x and y axes. For the horizontal bar graph place the frequency scale on the x axis, and for the vertical bar graph place the frequency scale on the y axis.

B.     Draw the bars corresponding to the frequencies as below.

1.      The modal rainfall year is 1993.

For any further advice on your studies or any challenge on this post, please feel free to contact me at: dzaazo@gmail.com. I will appreciate it. 

Statistical graphs – Cumulative Frequency (Ogive)

Introduction

Having organized the data into a frequency distribution, you need to present them in graphical form. The purpose of graph in statistics is to convey the data to the viewers into pictorial form. The reason is that it is easier for most people to understand the meaning of data presented graphically than data presented numerically in frequency distributions or tables. This is especially true if users have little or no statistical knowledge.

Uses of statistical graphs

1.      Statistical graphs can be used to analyse a data or described it.

2.       They are used to get the audience’s attention in a speaking presentation.

3.      They are also used to discover a pattern in a situation over a period of time.

4.      Statistical graphs are used to summarize a data.

The Ogive:

This type of graph is called cumulative frequency graph, or ogive. The cumulative frequency is the sum of the frequencies accumulated up to the upper boundary of a class in the distribution. The graph is drawn by plotting the cumulative frequency on the vertical axis against the upper class boundary [marks less that, less than class etc] on the horizontal axis.

Definition: The Ogive is a graph that represents the cumulative frequencies for the classes in a frequency distribution.

The example below shows the procedure for constructing an ogive.

Example one:

The following table shows the distribution of the marks scored by 200 candidates in an examination.

Marks	0-9	10-19	20-29	30-39	40-49	50-59	60-69	70-79	80-89
Frequency	3	18	20	25	34	50	25	15	10

Construct a cumulative frequency table and use it to draw a cumulative frequency curve for the distribution.

Solution

Steps:

1.      Find the cumulative frequency for each class.

2.      Draw the x and y axes. Label the x axis with the upper class boundaries. Use an appropriate scale for the y axis to represent the cumulative frequencies. (Depending on the numbers in cumulative frequency columns, scales such as 0,1,2,.., or 5,10,15,... can be used. Do not label the y axis with the number in the cumulative frequency column.) In this example, a scale of 0, 20, 40, 60 ... will be used.

3.      Plot the cumulative frequency at each upper class boundary. Upper boundaries are used since the cumulative frequencies represent the number of data values accumulated up to the upper boundary of each class.

4.      Starting with the first upper boundary, connect adjacent points with line segments. Then extend the graph to the first lower class boundary, on the x-axis.

Marks less than	Frequency	Cumulative Frequency
9.5	3	3
19.5	18	21
29.5	20	41
39.5	23	64
49.5	34	98
59.5	50	148
69.5	25	173
79.5	15	188
89.5	10	198
99.5	2	200

Statistical graphs – Frequency Polygon

Introduction

Having organized the data into a frequency distribution, you need to present them in graphical form. The purpose of graph in statistics is to convey the data to the viewers into pictorial form. The reason is that it is easier for most people to understand the meaning of data presented graphically than data presented numerically in frequency distributions or tables. This is especially true if users have little or no statistical knowledge.

Uses of statistical graphs

1.      Statistical graphs can be used to analyse a data or described it.

2.       They are used to get the audience’s attention in a speaking presentation.

3.      They are also used to discover a pattern in a situation over a period of time.

4.      Statistical graphs are used to summarize a data.

The frequency polygon:

The frequency polygon is a graph that displays the data by using lines that connect point plotted for the frequencies at the midpoint of the classes. The frequencies are represented by the heights of the points. They are drawn to have zero frequencies. We note that, frequency polygon can also be drawn without the bars. See fig below:

The example below shows the procedure for constructing a frequency polygon.

Example one:

The following is a frequency distribution of masses of parcels in a local post office.

Mass kg	10-19	20-29	30-39	40-49	50-59	60-69	70-79	80-89	90-99
No. Of parcels	2	4	7	8	11	9	5	4	3

a.       Draw a frequency polygon for the distribution.

Solution

Steps:

1.      Find the midpoints of each class. Recall that midpoints are found by adding the upper and lower boundaries and dividing by 2; (9.5 + 19.5) ÷ 2 = 14.5, (19.5 + 29.5) ÷ 2 = 24.5 and so on.

2.      Draw the x and y axes. Label the x axis with the midpoint of each class, and then use a suitable scale on the y axis for the frequencies.

3.      Using the midpoints for the x-values and the frequencies as the y-values, plot the points.

4.      Connect adjacent points with line segments. Draw line back to the x axis at the beginning and end of the graph, at the same distance that the previous and next midpoints would be located. See the table below.

Mass (kg)	Mid-mass (x)	Frequency
10-19	14.5	2
20-29	24.5	4
30-39	34.5	7
40-49	44.5	8
50-59	54.5	11
60-69	64.5	9
70-79	74.5	5
80-89	84.5	4
90-99	94.5	3

For any further advice on your studies or any challenge on this post, please feel free to contact me at: dzaazo@gmail.com. I will appreciate it.