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Grade 10 Mathematics Teachers’ Book

INNODEMS

Subsection 3.1.1 Introduction to Statistics

In everyday life, individuals, organizations, and governments make decisions based on information. Schools analyse learners’ performance, hospitals record patient data, businesses track sales trends, farmers decide when to plant crops and governments collect population data to plan development projects. This systematic process of gathering, organizing, analysing, and interpreting the information above is known as Statistics.
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Statistics enables us to transform raw data into meaningful information that supports informed decision-making. Understanding where data comes from and how it is collected is essential before organizing, representing, and interpreting it.
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Subsubsection 3.1.1.1 Sources of Data

Learner Experience 3.1.1.

Work in groups
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A teacher assigned students a research topic on the effects of social media on teenage mental health in Kenya.
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(a)
Suggest one potential primary data collection method that could be used.
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(b)
Suggest one potential secondary data source that could be used.
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(c)
What is the difference between primary and secondary data?
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(d)
Why is secondary data important for research and decision-making?
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(e)
Discuss and share with other groups.
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Key Takeaway 3.1.3.

Data is a collection of facts, figures, numbers, observations, measurements, or descriptions that can be recorded, stored, and used to study or understand something.
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There are two primary categories of data sources: primary data and secondary data.
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  • Primary data is collected firsthand by the researcher or investigator specifically for the current study.
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  • Secondary data is information that has already been collected by someone else for a different purpose and is now used by the researcher.
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Example 3.1.4.

Classify the following as primary or secondary data sources:
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  1. A student conducts a survey to find out the favorite sports of their classmates.
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  2. A teacher uses last year’s national exam results to analyze student performance trends.
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  3. A researcher reads a government report on the most common diseases in Kenya.
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  4. A doctor observes a patient’s symptoms and records them for a medical study.
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  5. A scientist conducts an experiment to test the growth rate of plants under different conditions.
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Solution.
  1. Primary because the student is collecting first-hand data directly from people.
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  2. Secondary because the exam results were already collected and recorded by an external body.
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  3. Secondary because The report was collected and published by someone else for a different purpose.
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  4. Primary because The doctor is directly collecting new data from real-life observation.
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  5. Primary because The scientist is generating new data through an experiment.
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Example 3.1.5.

A community group wants to understand the needs of youth in their area.
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  1. What primary data collection methods could the group use?
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  2. What problems might they have when trying to find this information?
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  3. How can they use the information they find to help the community?
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  4. What secondary data sources could be useful to this community group?
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Solution.
  1. Focus groups, surveys, interviews.
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    • They can start new programs for young people.
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    • They can tell leaders what young people need.
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    • Academic studies on youth issues.
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    • Government reports on youth.
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Checkpoint 3.1.6.

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Checkpoint 3.1.7.

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Exercises Exercises

1.
Grade \(10\) students from Korinyang Primary School went to Lake Nakuru National Park and counted the flamingos they saw for their Biology project.
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  1. Is this a primary or secondary data source?
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  2. Give reason.
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Answer.
  1. Primary data source.
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  2. The students collected the data themselves through direct observation and counting.
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2.
In a market, a shop owner watches what customers buy most often and looks for trends based on what they see in the store.
  1. Which sources of data can the shop owner use to collect the data?
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Answer.
Direct observation, sales transaction records, and customer surveys/interviews.
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3.
What are the advantages of using secondary data over primary data in some research situations?
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Answer.
It is faster to obtain, cheaper than conducting new research, and provides access to larger historical datasets.
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Subsubsection 3.1.1.2 Methods of Data Collection

Learner Experience 3.1.2.

Work in groups
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  1. The following data represents the number of hours people spend watching television per week.
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    • \(0 - 5\) hours: \(20\) people
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    • \(6 - 10\) hours: \(35\) people
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    • \(11 - 15\) hours: \(25\) people
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    • \(16 - 20\) hours: \(10\) people
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  2. Create a table to organize this data.
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  3. What type of data collection method was most likely used to gather this data?
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  4. What are some other questions that could be asked to further explore this topic?
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  5. Discuss and share with other groups.
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Key Takeaway 3.1.9.

  • Methods of collecting data help us gather information.
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  • Data can be collected using:
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    Primary data collection methods (interviews, observations, questionnaires, experiments) involve gathering new data directly from sources.
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    Secondary data collection methods involve using existing data records.
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    1. Surveys/Questionnaires: A set of questions designed to gather information from a group of people. They can be conducted in person, over the phone, or online.
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    2. Interviews: A conversation between an interviewer and a respondent to gather detailed information on a specific topic.
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    3. Observations: The process of watching and recording behaviors or events as they occur in their natural setting.
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    4. Experiments: A method of collecting data by manipulating one variable to determine its effect on another variable.
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    5. Existing records (Secondary data): The use of existing data that has been collected by someone else for a different purpose. This can include government reports, academic studies, and historical records.
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Example 3.1.10.

A student wants to find out the most popular extracurricular activities among their classmates.
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  1. What data collection method would be most appropriate?
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  2. What are two examples of specific questions they could ask?
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Solution.
  1. Survey/Questionnaire.
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  2. Questions for students to ask are;
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    • What extracurricular activities do you participate in?
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    • How often do you participate in these activities?
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Example 3.1.11.

A local bakery, conducted a study asking customers about their favorite types of pastries. The results are:
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  1. What type of data collection method was most likely used to gather this data?
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  2. What is the most popular type of pastry among customers?
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  3. What percentage of customers prefer either Cakes or Cookies?
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  4. What type of pastry is the least popular among customers?
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Solution.
  1. A survey.
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  2. Cakes
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  3. \(45\% \) + \(30\%\)= \(75\%\)
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    Therefore, the percentage of customers who prefer either Cakes or Cookies are \(75\%\)
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  4. Doughnuts
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Checkpoint 3.1.12.

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Checkpoint 3.1.13.

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Exercises Exercises

1.
Which data collection method would be most suitable for finding out the most common types of litter found in your school compound?
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  1. Interviews
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  2. Surveys sent to parents
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  3. Observations
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  4. Analyzing government reports
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Answer.
c) Observations.
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2.
Describe one ethical consideration you should keep in mind when conducting interviews with community members.
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Answer.
Obtaining informed consent from the participants.
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3.
Why is it important to keep accurate records when conducting observations?
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Answer.
To ensure the reliability and validity of the final analysis.
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4.
Give one example of a situation where you would use secondary data collection in a Geography class.
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Answer.
Using a government census report to study population density in a region.
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