Lesson Notes By Weeks and Term v3 - Junior Secondary 2
Data presentation
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Data presentation
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Subject: General Mathematics
Class: Junior Secondary 2
Term: 2nd Term
Week: 3
Theme: Everyday Statistics
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Present data in an or dered form Construct frequency tables from any given data Draw pie charts Read in for mation from pie chart Generate and use data for statistical purposes In terpret and use tables, charts, records and schedules.
is proportional to the quantity it represents.
Steps to Construct a Pie Chart:
1. Calculate the total frequency (sum of all data values). This represents the whole (360° of the circle).
2. Calculate the angle for each sector: For each category, use the formula: Angle of sector = (Frequency of category / Total frequency) 360°
3. Draw a circle using a compass.
4. Draw a radius from the center to the top (or any convenient starting point).
5. Use a protractor to measure and draw the calculated angle for the first sector from the drawn radius.
6. Draw another radius to mark the end of the first sector.
7. Repeat steps 5 and 6 for all subsequent sectors, using the last drawn radius as the starting line for the next angle.
8. Label each sector clearly with its category name and (optional) its frequency or percentage. Give the chart a clear title.
Worked Example 3: Drawing a Pie Chart The table below shows the favourite food of 40 students in a JSS2 class: | Food | Number of Students (Frequency) | | :-------- | :----------------------------- | | Jollof Rice | 15 | | Amala | 10 | | Pounded Yam | 8 | | Akpu | 7 | | Total | 40 | Solution:
1. Total frequency = 40 students.
2. Calculate angles for each sector: Jollof Rice: (15 / 40) 360° = 0.375 360° = 135° Amala: (10 / 40) 360° = 0.25 360° = 90° Pounded Yam: (8 / 40) 360° = 0.20 360° = 72° Akpu: (7 / 40) 360° = 0.175 360° = 63° (Check: Sum of angles = 135° + 90° + 72° + 63° = 360°)
3. Draw the pie chart: Draw a circle with a compass. Draw a starting radius. From this radius, measure 135° for Jollof Rice. From the new radius, measure 90° for Amala. Continue with 72° for Pounded Yam and 63° for Akpu. Label each sector appropriately. (Teacher should illustrate this on the board using a large compass and protractor). 2.
5. Reading Information from Pie Charts Interpreting pie charts involves understanding the proportions represented by each sector and using this to answer questions or calculate actual values.
Steps to Read Information:
1. Examine the title to understand what the chart represents.
2. Identify the categories and their corresponding angles or percentages.
3. Relate parts to the whole: The entire circle represents 100% or 360°.
4. Calculate unknown values: If percentages are given, and the total value is known, calculate the value of a sector: (Percentage / 100) Total value. If angles are given, and the total value is known, calculate the value of a sector: (Angle of sector / 360°) Total value. If a sector's value and angle/percentage are known, find the total value: Total value = (Known value / Proportion) where proportion is (angle/360°) or (percentage/100).
Worked Example 4: Reading Information from a Pie Chart A pie chart shows how a student, Segun, spends his N7,200 monthly allowance.
The angles for some expenses are given: Food (120°), Transport (90°), School Supplies (60°). The remaining portion is for Savings.
Questions: a) What is the angle for Savings? b) How much does Segun spend on Food? c) How much does Segun save?
Solution: a)
Angle for Savings: Total angle in a circle = 360° Sum of given angles = 120° (Food) + 90° (Transport) + 60° (School Supplies) = 270° Angle for Savings = 360° - 270° = 90° b)
Amount spent on Food: Total allowance = N7,200 Angle for Food = 120° Amount on Food = (Angle for Food / 360°) Total allowance Amount on Food = (120 / 360) N7,200 Amount on Food = (1/3) N7,200 = N2,400 c)
Amount Segun Saves: Angle for Savings = 90° (from part a) Amount Saved = (Angle for Savings / 360°) Total allowance Amount Saved = (90 / 360) N7,200 Amount Saved = (1/4) N7,200 = N1,800 *(Alternatively, for Savings = 360° - 270° = 90° b)
Amount spent on Food: Total allowance = N7,200 Angle for Food = 120° Amount on Food = (Angle for Food / 360°) Total allowance Amount on Food = (120 / 360) N7,200 Amount on Food = (1/3) N7,200 = N2,400 c)
Amount Segun Saves: Angle for Savings = 90° (from part a) Amount Saved = (Angle for Savings / 360°) Total allowance Amount Saved = (90 / 360) N7,200 Amount Saved = (1/4) N7,200 = N1,800 (Alternatively, calculate for Transport and School Supplies, then subtract from total: Transport: (90/360) 7200 = N1,800 School Supplies: (60/360) 7200 = N1,200 Total spent = N2400 + N1800 + N1200 = N5400 Savings = N7200 - N5400 = N1,
8
0
0. This confirms the calculation.) 2.
6. Generating and Using Data for Statistical Purposes Data presentation methods like frequency tables and pie charts are fundamental tools in statistics.
They allow for: Summarization: Condensing large datasets into manageable summaries.
Visualization: Making data easier to understand and interpret visually.
Identification of Trends: Spotting patterns, frequencies, and proportions that might not be obvious in raw data.
Decision Making: Providing a basis for informed decisions in various fields (e.g., business, public health, government policy, education). 2.
7. Interpreting and Using Tables, Charts, Records and Schedules Students should understand that data presentation is not limited to frequency tables and pie charts. Bar charts, pictograms, line graphs, and various administrative records (e.g., class attendance register, flight schedules, market price lists) are all forms of data presentation. The skills learned in interpreting pie charts (understanding proportions, values, and titles) are transferable to other forms of data presentation, enabling students to extract relevant information and apply it in different contexts. --- 2.
1. Data Data refers to a collection of facts, figures, observations, or information that has been gathered. When data is collected, it is often in a raw, unorganized form. To make it meaningful, it needs to be processed and presented.
Raw Data: Data that has just been collected and has not yet been organized or analyzed.
Example: The number of yams sold by a farmer over 10 days: 15, 20, 12, 18, 20, 15, 25, 12, 18, 20. 2.
2. Presenting Data in Ordered Form Ordering data involves arranging it in a specific sequence, usually in ascending order (from smallest to largest) or descending order (from largest to smallest). This helps to quickly identify the minimum, maximum, and repeated values, making the data easier to understand.
Steps:
1. Scan the raw data.
2. Choose to arrange in ascending or descending order.
3. Write out the data points in the chosen order.
Example 1: The marks obtained by 15 students in a JSS2 Mathematics test (out of 20) are: 12, 15, 10, 18, 12, 14, 15, 10, 16, 12, 18, 14, 15, 16,
1
2. To present this data in ascending order: First, identify the smallest mark (10) and the largest mark (18).
Count the occurrences of each mark: 10 (2 times) 12 (4 times) 14 (2 times) 15 (3 times) 16 (2 times) 18 (2 times)
Arranged in ascending order: 10, 10, 12, 12, 12, 12, 14, 14, 15, 15, 15, 16, 16, 18, 18. 2.
3. Constructing Frequency Tables A frequency table is a way of organizing raw data by showing how often each data item occurs.
It consists of three columns: the data item, tally marks, and frequency.
Key Terms: Tally Marks: Vertical strokes used to count the occurrences of each data item. For every group of four vertical strokes, the fifth one is drawn horizontally across the first four (e.g., |||| represents 5).
Frequency: The number of times a particular data item appears in a dataset.
Steps to Construct a Frequency Table:
1. List all unique data items in the first column (usually in ascending order).
2. Go through the raw data item by item, and for each item, place a tally mark ( | ) in the second column next to its corresponding data item.
3. After all data items have been tallied, count the tally marks for each row and write the total in the third column (Frequency).
4. Sum the frequencies to ensure it matches the total number of data points.
Worked Example 2: Constructing a Frequency Table The number of goats owned by 20 families in a Nigerian village are recorded as follows: 3, 5, 2, 4, 3, 6, 2, 5, 3, 4, 3, 5, 2, 6, 4, 3, 5, 2, 4,
3. Solution:
1. Identify unique data items: 2, 3, 4, 5, 6.
2. Create the table and start tallying: | Number of Goats | Tally Marks | Frequency | | :-------------- | :---------- | :-------- | | 2 | |||| | 4 | | 3 | |||| | | 6 | | 4 | |||| | 4 | | 5 | |||| | 4 | | 6 | || | 2 | | Total | | 20 | (Check: Sum of frequencies = 4+6+4+4+2 = 20, which matches the total number of families, 20). 2.
4. Drawing Pie Charts A pie chart (or circle graph) is a circular statistical graphic, which is divided into slices to illustrate numerical proportion. In a pie chart, the arc length of each slice, and consequently its area and central angle, is proportional to the quantity it represents.
Steps to Construct a Pie Chart:
1. Calculate the total frequency (sum of all data values). This represents the whole (360° of the circle).
2. Calculate the angle for each sector: For each category, use the formula: Angle of sector = (Frequency of category / Total frequency) * 360°
3. Draw a circle using a compass.
4. Draw a radius from the center to the top (or any convenient starting point).
5. Use a protractor to measure and draw the calculated angle for the 3.
1. Introduction (10 minutes)
Teacher Activity: Begin by asking students how they might present information about the number of students who walk, cycle, or use public transport to school without just listing names. Discuss the challenges of understanding raw, unorganized data. Introduce the concept of data presentation as a way to make data clear and meaningful.
Student Activity: Engage in a brief discussion about different ways they see information presented (e.g., news charts, election results). Respond to teacher questions. 3.
2. Presenting Data in Ordered Form (15 minutes)
Teacher Activity: Provide a set of raw data (e.g., ages of 20 students in years: 13, 12, 14, 13, 11, 12, 13, 14, 12, 11, 13, 14, 12, 13, 11, 12, 13, 14, 12, 11). Demonstrate how to arrange this data in ascending order on the board, emphasizing clarity and systematic arrangement.
Student Activity: Copy the raw data and attempt to order it independently or in pairs. Compare their ordered lists with the teacher's example. 3.
3. Constructing Frequency Tables (25 minutes)
Teacher Activity: Using the ordered data from the previous activity or a new, simple dataset (e.g., shoe sizes of 15 students), demonstrate step-by-step how to construct a frequency table. Emphasize the use of tally marks and how to count them correctly. Show how to sum the frequencies to cross-check with the total number of data items.
Student Activity: In groups, students will be given a new set of raw data (e.g., number of siblings each student has). Each group constructs a frequency table. Groups then share their tables and compare results, discussing any discrepancies. 3.
4. Drawing Pie Charts (40 minutes)
Teacher Activity: Present a simple frequency table (e.g., favorite colours of 30 students). Guide students through the calculation of angles for each sector on the board. Emphasize the formula (frequency/total frequency) * 360°. Using a large compass and protractor on the board, demonstrate the drawing of a circle and the accurate measurement of angles for each sector. Stress the importance of clear labels and a title. Circulate the classroom to provide individual assistance.
Student Activity: Copy the frequency table and calculate the angles for each sector. Using their compasses and protractors, students draw their own pie charts in their notebooks. Students label their charts clearly and give them appropriate titles. Peer-check each other's work for accuracy and neatness. 3.
5. Reading Information from Pie Charts (20 minutes)
Teacher Activity: Display a pre-drawn pie chart (e.g., showing the sources of income for a typical Nigerian household or the distribution of crops in a local farm, with angles or percentages given). Ask specific questions that require students to interpret the chart (e.g., "Which source contributes most?", "If the total income is N50,000, how much comes from petty trading?"). Guide them through the calculations involved.
Student Activity: Students will answer the questions based on the displayed pie chart. They will present their calculations and reasoning. Engage in a class discussion about their interpretations. 3.
6. Generating and Using Data for Statistical Purposes / Interpreting Tables, Charts, Records and Schedules (10 minutes)
Teacher Activity: Lead a discussion on how the skills learned in this lesson (ordering data, constructing frequency tables, drawing/reading pie charts) are useful in real-life situations. Provide examples such as school records, community surveys, or market research. Explain that these tools help us make sense of information and inform decisions.
Student Activity: Brainstorm other examples of where data presentation is useful in their community or Nigeria at large. Share their ideas with the class. ---
Community Health Statistics: Data presentation can be used to show the prevalence of certain diseases (e.g., malaria, cholera) in different age groups or areas within a Nigerian community. A pie chart could represent the proportion of different types of illnesses reported at a local health center over a month. This helps community health workers and government agencies to allocate resources effectively for prevention and treatment campaigns, e.g., targeting areas with higher prevalence for mosquito net distribution.
Agricultural Market Analysis: Farmers in Nigeria can benefit from understanding data presentation. For instance, data on the monthly harvest of different crops (e.g., maize, cassava, yams) in a particular season can be presented in a pie chart to show which crop is produced in the largest quantity. Similarly, frequency tables can track the prices of farm produce over time, helping farmers decide when to sell their goods for maximum profit. This directly relates to market dynamics and economic decision-making for individuals and agricultural cooperatives.
School Management and Performance: School administrators frequently use data presentation for various purposes. A school could use a frequency table to record student attendance for a term, or a pie chart to show the proportion of students involved in different extracurricular activities (e.g., Football Club, Debate Society, Cultural Troupe). This helps in resource allocation, identifying areas for improvement, and understanding student engagement. For example, if a small percentage are involved in science clubs, the school might organize more science-related activities. ---