Purpose of Statistics and Methods of Data Collection for JSS 1

Needs for Statistics

Performance Objectives

By the end of the lesson, students should be able to:

1. list the purposes of statistics;
2. collect data;
3. recognize the uses of statistics for planning purposes;
4. apply the chance events or probability in everyday life;
5. recognize the uses of statistics for prediction purposes;
6. perform a simple experiment with dice.

What is Statistics?

Statistics is a branch of mathematics that deals with collecting, organising, analysing, interpreting, and presenting facts and figures. These facts and figures are called data. Statistics helps people to understand information better and make informed decisions.

Imagine a situation where a school wants to know the favourite subjects of its JSS1 students. To find this out, the school would need to collect information (data) from all the students, organise it, and then look at the results to see which subject is most popular. This entire process involves statistics.

Purposes of Statistics

Statistics is used in many areas of life to help us understand the world around us. The main purposes of statistics include:

1. For Planning: Statistics helps individuals, schools, businesses, and governments to plan for the future. By looking at past and present data, better plans can be made.
2. For Prediction: Statistics helps to forecast or guess what might happen in the future based on current and past information. This is useful in many situations, like predicting weather or election results.
3. For Decision Making: When people have collected and organised data, they can use it to make better choices. Decisions based on facts are usually more reliable than decisions based on guesswork.
4. For Simplification of Data: Statistics helps to simplify large amounts of data into a form that is easy to understand. Instead of looking at many individual numbers, statistics can present information clearly, often using tables or simple summaries.

Data Collection Strategy

Data collection is the process of gathering information from different sources. To use statistics effectively, it is important to collect data in a proper way. There are different strategies for collecting data:

1. Direct Observation: This involves watching and recording events or characteristics as they happen. For example, counting the number of cars that pass a school gate in an hour.
2. Surveys or Questionnaires: This involves asking people questions and recording their answers. For example, asking JSS1 students about their favourite food.
3. Experiments: This involves setting up a controlled situation to see what happens. For example, rolling a dice many times and recording the outcomes.
4. Using Existing Records (Secondary Data): This involves gathering data that has already been collected by others. For example, looking at past school attendance records or browsing results from examination bodies like NECO or WAEC.

When collecting data, it is important to be organised and accurate to ensure the information is useful.

Data for Planning Purposes

One of the most important uses of statistics is for planning. Good planning helps to achieve goals and avoid problems. Data provides the necessary information to make these plans effective.

Examples of how data is used for planning include:

1. School Planning: A school might collect data on the number of students in each class to plan how many teachers are needed or how many textbooks to buy. Data on student performance can help plan extra lessons for subjects where students are struggling.
2. Community Planning: Local government councils use data on population size, age groups, and common illnesses to plan for new schools, hospitals, or markets in a community.
3. Business Planning: Businesses collect data on what products customers buy most often to plan what to produce more of. They also use data to decide where to open new shops.
4. Personal Planning: Individuals might track their spending habits (data) to plan a budget and save money for a specific goal.

Data for Prediction Purposes

Statistics helps us to make educated guesses about future events. This is called prediction. Predictions are not always perfectly accurate, but they help us prepare for what might happen.

Examples of how data is used for prediction include:

1. Weather Forecasts: Meteorologists (weather scientists) collect data on temperature, rainfall, wind speed, and air pressure over many years. They use this data to predict whether it will rain tomorrow or if the weather will be sunny.
2. Sports Outcomes: Sports analysts use data on a team’s past performance, player statistics, and opponent’s strengths to predict the likely winner of a match.
3. Election Results: Before an election, researchers collect data from a sample of voters to predict which candidate is likely to win.
4. Disease Outbreaks: Health organisations use data on the spread of diseases to predict where and when an outbreak might occur, allowing them to prepare medical supplies and personnel.

Chance Events and Probability in Everyday Life

Many events in life involve chance. This means we cannot be certain of the outcome. Probability is the measure of how likely an event is to happen. When we use statistics for prediction, we often consider the probability of different outcomes.

Examples of chance events in everyday life include:

1. Flipping a coin: It can land on heads or tails.
2. Rolling a dice: It can land on any number from 1 to 6.
3. Winning a lottery: The chances are usually very small.
4. Whether it will rain tomorrow: There is a certain probability of rain based on weather data.

Understanding chance helps us to make better predictions and decisions, even when outcomes are not certain.

Decision Making from Collected Data

After data has been collected and organised, it becomes a powerful tool for making decisions. Good decisions are based on facts, not just feelings or assumptions.

For example, if a school collects data showing that many students arrive late, the school management can decide to start classes five minutes later or introduce a reward system for punctuality. If a farmer collects data on which crops grow best in a certain soil type, they can decide to plant more of those successful crops.

The process of decision making using data involves:

1. Identifying the problem or question.
2. Collecting relevant data.
3. Organising and simplifying the data.
4. Analysing the data to find patterns or insights.
5. Using these insights to make an informed decision.

Simplification of Collected Data

Raw data, especially when there is a lot of it, can be difficult to understand. Statistics helps to simplify this data so that it can be easily interpreted. At this level, simplification often involves organising data into simple tables or using tally marks.

Using Tally Marks

Tally marks are a simple way to count and record data as it is collected. Each vertical line represents one item, and the fifth item is represented by a diagonal line across the previous four, making a group of five.

For example, if students are asked about their favourite fruits, the responses can be recorded using tally marks:

This table simplifies the data, making it easy to see that banana is the favourite fruit among these students.

Practical Application: Collecting Data

Collecting data accurately is a key skill in statistics. This procedure outlines how to collect data through a simple survey.

The required materials are:

1. A pen or pencil
2. A notebook or paper

The procedure involves the following steps:

1. Choose a Topic: Decide what information you want to collect. For example, “Favourite colours of classmates.”
2. Prepare Questions: Formulate a simple question. For example, “What is your favourite colour?”
3. Identify Your Sources: Decide who you will ask. For example, 10 classmates.
4. Record Responses: As each classmate tells you their favourite colour, record it using tally marks in a table like the one shown above. Create columns for “Colour,” “Tally Marks,” and “Number of Students.”
5. Count and Summarise: After asking all 10 classmates, count the tally marks for each colour and write the total number in the “Number of Students” column.
6. Review: Look at your collected data. Which colour is most popular? Which is least popular?

Practical Application: Performing a Simple Experiment with Dice

This experiment helps to understand chance events and how to record outcomes.

The required materials are:

1. One standard six-sided dice
2. A pen or pencil
3. A notebook or paper

The procedure involves the following steps:

1. Prepare a Table: On your paper, create a table with two columns: “Outcome (Number Rolled)” and “Tally Marks.” List the possible outcomes (1, 2, 3, 4, 5, 6) in the first column.
2. Roll the Dice: Gently roll the dice onto a flat surface.
3. Record the Outcome: Observe the number that appears on the top face of the dice. Make a tally mark next to that number in your table.
4. Repeat: Roll the dice many times (e.g., 20 or 30 times). Each time, record the outcome with a tally mark. The more times you roll, the better your data will be.
5. Count and Summarise: After all the rolls, count the tally marks for each number and add a third column to your table for “Frequency” (how many times each number appeared).
6. Analyse the Results: Look at your table. Did each number appear roughly the same number of times? Or did some numbers appear more often than others? This shows how chance works in a simple experiment.