Introduction to statistics

The Purpose of Statistics

Definition of Statistics

Statistics is a branch of science that is concerned with the methods of collecting, organizing, presenting and analyzing data for a specific purpose.

Information in raw or unorganized form (such as alphabets, numbers, or symbols) that refer to, or represent, conditions, ideas, or objects. Data is limitless and present everywhere in the universe.

Statistics is the branch of mathematics, which deals with the study of data. It involves:

1. Gathering (i.e. collecting) data
2. Sorting and tabulating data
3. Presenting data visually by means of diagrams (charts, tables and graphs)
4. Interpreting results.

Statistics is known to provide useful information in our everyday life:

1. For record keeping
2. To forecast or predict future events
3. For decision making
4. For planning purposes
5. To gather useful information this can be passed from one source to another.

Collection of Data for Planning Purposes

Planning is one of the reasons for collecting data.

Examples include;

• The Daily Export Report of barrels of petrol enables the government of Nigeria to plan the budgets. This is called economic planning.
• Statistics about the availability of potable drinkable water can inform State and District planners whether or not to budget for pumps and pipelines.
• Statistics about the trend in school enrollment could inform the school management about the schools where urgent expansions are needed.
• Statistics about the prevalence of HIV/AIDS among the citizenry could inform the relevant agency as to how to arrest the spread of the virus/disease.

CLASS ACTIVITY

A shop keeper makes record of his sales for the day. The records are as shown in the table below. This is an example of statistics used for planning purpose/decision making.

Which size sells more than the other?

Which size gives more profit for the day?

If you were the shop keeper, which size would you plan to buy more on the following day? Give reasons.

The Need for Collecting Data for Analysis Purposes

Collection of data from time to time helps to analyze situations. For example, statistics shows that malaria is responsible for about half the deaths of African children under the age of five. The minister of health in Nigeria revealed that the number of tuberculosis in Nigeria increased from 31 264 in 2002 to 90 307 in 2008. The number of people who died of Aids in South Africa in 2007 is about 350 000. This means Aids claimed nearly 1000 lives every day.

Example 2:

The table below shows a survey of the favorite subjects of students in basic 2.

(i) What subject do the girls like most?

(ii) How many more boys than girls like Math?

(iii) What fraction of the girls like Math?

(iv) What percentage of the students are girls?

Solution:

(i) From the table above, English is the favourite subject of the girls.

(ii) 30 boys like maths, while 25 girls like maths. Therefore, 5 more boys than girls like maths.

(iii) The total number of girls = 35 + 25 + 15 = 75

The fraction of the girls that like maths = no. of girls who like mathtotal no. of girls=2575=13

(iv) The percentage of the students that are girls = total no. of girlstotal no. of students×100

Total number of boys = 25 + 30 + 20 = 75

Total number of students = 75 boys + 75 girls

= 150 students

The percentage of girls = 75150×100=12×100=50%

CLASS ACTIVITY

The table below shows the distribution of science teachers in a particular private senior secondary school in the suburb of Abuja.

(i) Which subject has the highest number of teachers?

(ii) Which subject has the least number of teachers?

(iii) What is the total number of science teachers in the school?

(iv) What is the average number of teachers per Science subject in the school?

The Need for Collecting Data for Prediction Purposes

The statistical charts and tables we do see on television and in the newspapers (or magazines), provide useful information which can be used to make forecast and predictions for the future. For example, the number of students enrolment in secondary and post secondary schools this year can help the government plans the number of new jobs to be created in five years’ time.

Example 3:

A food seller collects the following sales data for the week.

Will you support her decision to stop selling tuwo and yam? On what prediction do you think she based her decision?

CLASS ACTIVITY

1. If your village played with another village 10 times in the past, with 9 wins and 1 loss, what is your prediction for the next match?
2. Give some reasons why you think a school principal should know the number of students in

his school?

Collection of Data in Class

Since statistics cannot exist without data, you will need to collect data first. Collection of data involves counting and recording data clearly in a way that is useful.

Example:

Teacher should write down the names of students in his/her class against their individual ages.

CLASS ACTIVITY

1. Find out the number of students in your school. Make a table to show the number of students in each level.
2. How many males and female students do you have in your school?
3. How many male and female teachers are in your school?

Data Presentation

Rank-ordered List

Rank order means arranging data values from the highest to the lowest.

Example:

Some JCSE students scored these grades in a revision test: C, B, D, A, C, C, E, B, D, F, B, D, E, C, A, C, D, B. Represent the data in rank order.

Solution:

Here is the rank order list from A to F:

A, A, B, B, B, B, C, C, C, C, C, D, D, D, D, E, E, F

Frequency Table

A frequency table shows the number of times a value appears. A frequency table can be prepared for a give data set data either vertically or horizontally.

Example:

In a class of 30 students seated in six rows of five students each, the class monitor records the following dates of births, row by row.

1. a) Represent the above data in a frequency table.

(b) How many students were born on Tuesdays?

(c) In what date were most students born?

(d) In what date were the least number of students born?

Solution:

Rank Ordered Lists Versus Frequency Tables

Two students were asked to collect data about the type of vehicles, as they passed by. The data collected were presented in two different ways, as follows:

A. car, lorry, lorry, motorcycle, car, motorcycle bicycle, bus, lorry, car, bus, bus, bus

The first student presented his data by listing the vehicles as they pass by. This method is not very reliable. The method adopted by the second student is the best because he cannot miss any vehicle in his recording, especially by ‘TALLY’.