Statistics: Making Sense of Numbers
Statistics is used in our daily life. We use statistical data to back our everyday decisions such as buying household goods, which are reliable to stock up on popular food during festivities. Many are fearful of statistics due to the complicated formulae. This unit is to help students grasp the fundamental concepts of statistics and understand what statistics mean to them in their daily lives. Students explore the question: How do numbers influence our lives?.
Students investigate how statistical analysis is used for various industries. They choose an activity or a business in and around the school and find out how they can apply statistics to help improve their businesses. They also learn how to calculate mode, median and mean using spreadsheet application. Students present their findings to the class or business manager using a multimedia presentation.
- Essential Question
How do numbers influence our lives?
- Unit Questions
Is statistics important to us?
How can we apply statistics in our daily lives?
How are mode, median, and mean values derived from the data useful to us?
- Content Questions
What is mode, median, and mean?
How do you calculate mode, median, and mean?
When do you use mode, median, and mean effectively?
View how a variety of student-centred assessments are used in the Statistics: Making Sense of Numbers Unit Plan. These assessments help students and teachers to set goals; monitor students’ progress; provide feedback; assess thinking, processes, performances, and products and reflect on learning throughout the learning cycle.
Introduce the unit by posing a few questions related to numbers and statistical data from the gauge students’ needs presentation (ppt). The discussion is used to gauge the prior knowledge of the students and their readiness to the topic.
The discussion also leads the students to the Essential Question: How do numbers influence our lives? Have students brainstorm the ideas and generate a list on chart paper or white board. Then, hold a whole-class discussion around the question asking students to give examples of numbers used in their lives. Keep this list visible throughout the unit.
Using statistics introduction presentation (ppt), explain to students that they will be learning about mode, median and mean. Show the statement, “Statistics is a science of collecting, organising, and analysing data”. Find out from students what do they think of the statement and have them explain it in their own words.
Present the Unit Question: Is statistics important to us? Allow time for students to write and discuss the prompts in the presentation. Ask students if they are able to relate how statistics is used in their lives. Discuss some relevant statistical examples used in their daily lives. Some of the examples are mobile phone usage for teenagers, average number of SMS sent by Malaysians and the music top chart lists.
Discuss what is mode, median and mean. Have students brainstorm ideas why mode, median and mean is used in statistics. Show students how to obtain and analyse values of mode, median and mean from a frequency table. Ask students whether all data can be used to extract mode, median and mean. Have students name a few examples that use mode, median and mean. Ask students whether they were aware of the use of mode, median and mean in statistical data. Ask for volunteers to share responses with the whole class.
Students are encouraged to research on the topic using some of the suggested sites such as robertniles* and purplemath*. Use statistics worksheet (doc) to re-examine students’ understanding on statistics as they read more about the statistical methods.
Statistics in Our Daily Lives
Engage students to brainstorm their answers to the Unit Question: How can we apply statistics in our daily lives? Elicit students’ responses whether statistical data has any meaning to them. Get the students to explore why some statistical data are more relevant than others.
In groups, have students investigate how statistical analysis is applied for various industries. Encourage students to select any one of the common industries, which may include the food, transportation, household goods, stationery, books, shoes and apparel. Other more specific industry could be environment, retail, engineering, construction, medical and entertainment. Using the school cooperative student assistant as an example, group members are asked to discuss whether the statistical data is useful and has meaning for the cooperative to help improve the business.
Becoming an Expert
Show a pictogram with the choice of flowers of a group of girls as below.
|represents 10 girls|
Have students calculate the mean, median and mode of the girls’ favourite flower. Tell students that they need to help a florist make orders according to their calculations of the girls’ favourite flower. Have students justify their decisions.
Introduce the project, Statistics: Making Sense of Numbers by telling students that they are going to choose an activity or a business (such as canteen, school co-op and bookshop) in their school where they can apply the statistical analysis to the school environment.
Use project rubric (doc) as a guide to explain the different aspects of the project and to determine how their work measures up to expectations. Hand out project plan (doc) to help students take ownership of their learning. The project plan guides students to identify goal, design strategy, make decision and track progress in the project.
Tell students that in order to have reliable statistical analysis, they will need to understand and remember the term, “GIGO – Garbage In, Garbage Out”, where meaningless data creates meaningless statistical values. Demonstrate how statistical data relies on representative samples.
Guide students on how they can use the Internet to research the type of activity or business they would like to apply their statistical knowledge. In order to help the students optimize their research, have student focus on the following questions:
- Is statistics important to us?
- How can we apply statistics in our daily lives?
- How are mode, median and mean values derived from the data useful to us?
- What type of statistical analysis can be done with the data?
- How can analysed statistical data be used to improve performance?
Provide time for students to research and have them record their information using electronic template or worksheet. The worksheet helps student organise their findings for upcoming presentation.
Applying Statistics to Solve Problems
After students have researched and gathered data for their selected activity or business, have them begin thinking and discussing how statistical analysis can be done with the data. Guide and assist students to identify the steps of data analysis. Distribute spreadsheet guide (doc) to help students calculate mode, median and mean using spreadsheet application.
Ask students to prepare a multimedia presentation (ppt) that address:
- Overview of their study on the selected activity or business
- Graphical representation of the data
- Statistical analysis
- Recommendations to improve the activity or business
Make sure students refer to the project rubric (doc) and use presentation checklist (doc) to plan their presentations. Conduct meeting with groups to discuss the presentations. Have students create their presentations once their storyboards have been approved.
When completed, allot time for students to present their projects. Have students observe other groups’ presentation using peer presentation feedback form (doc). Facilitate a brief discussion after each presentation.
Discovering Your Journey
As a final reflection activity, ask students use blog* to consider the Essential Question again: How do numbers influence our lives? They will compare how their thinking has changed since the beginning of the unit. Encourage students to examine their self-growth and discovery that resulted from their journey.
- Exposure to statistics
- Basic computer knowledge
- Internet research skills
- Provide extra time for research
- Consult with student frequently to check understanding and progress
- Provide opportunity for the students to interpret statistical analysis
- Have students take on a leadership role when working with groups
- Encourage student to include more advanced technical attributes in the presentation
This project idea has been developed by Toh Poi Seng and Yap Yih Yiu. A team of educators expanded the plan into the example you see here.