Lesson Notes By Weeks and Term v3 - Senior Secondary 1
Data Presentation
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Data Presentation
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Subject: General Mathematics
Class: Senior Secondary 1
Term: 1st Term
Week: 9
Theme: Statistics
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Collect tabulate and present data in meaningful form. Construct frequency tables. Identify and draw different types of linear graphs and bar-charts. Draw histogram with equal and unequal sides. Differentiate between bar-chart and histograms. Calculate the sectoral component of pie chart. Draw pie chart correctly. In terpret the pie chart. Construct frequency polygon of a given distribution.
Data: Raw facts, figures, or observations collected for a specific purpose.
Raw Data: Data collected in its original, unorganized form. E.g., a list of scores of 20 students in a Mathematics test.
Grouped Data: Data organized into classes or categories, often presented in a frequency distribution table.
Types of Data: Discrete Data: Data that can only take specific, countable values (usually whole numbers). E.g., number of children in a family, number of cars in a parking lot.
Continuous Data: Data that can take any value within a given range. E.g., height of students, temperature, weight of bags of rice.
Data Collection: The process of gathering information. Methods include observation, interviews, questionnaires, and existing records.
Tabulation: Organizing raw data into a structured format, typically using a tally system and frequency counts.
Tally Marks: Used to count occurrences. Each vertical line represents one occurrence, and the fifth line crosses the previous four (e.g., |||| ).
Frequency: The number of times a particular data value or class appears in a dataset. Class Mark (x) | | :------------- | :---------- | :-------------- | :--------------- | :------------- | | 15 - 19 | |||| | 4 | 14.5 - 19.5 | 17 | | 20 - 24 | |||| | 4 | 19.5 - 24.5 | 22 | | 25 - 29 | |||| | 5 | 24.5 - 29.5 | 27 | | 30 - 34 | |||| | 5 | 29.5 - 34.5 | 32 | | 35 - 39 | |||| | 5 | 34.5 - 39.5 | 37 | | 40 - 44 | |||| | 4 | 39.5 - 44.5 | 42 | | 45 - 49 | ||| | 3 | 44.5 - 49.5 | 47 | | Total | | 30 | | | This is correct. A frequency distribution table is a tabular arrangement of data that shows the frequency of each data value or class interval.
Class Interval: A range of values into which continuous data is grouped. E.g., 10-19, 20-
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9. Class Limit: The lowest and highest values in a class interval. E.g., for 10-19, 10 is the lower class limit, 19 is the upper class limit.
Class Boundary: The true boundary values separating adjacent classes. For a class like 10-19 and the next 20-29, the upper boundary of the first class and lower boundary of the next class will meet at 19.
5. Lower class boundary = Lower class limit - 0.5 (for integer data) Upper class boundary = Upper class limit + 0.5 (for integer data)
Example: For class 10-19, lower boundary = 9.5, upper boundary = 19.
5. For class 20-29, lower boundary = 19.5, upper boundary = 29.
5. Class Mark (Midpoint): The midpoint of a class interval. Class Mark = (Lower Class Limit + Upper Class Limit) / 2 Class Mark = (Lower Class Boundary + Upper Class Boundary) / 2 Class Width (Size): The difference between the upper and lower class boundaries of a class interval. Class Width = Upper Class Boundary - Lower Class Boundary Alternatively, it can be calculated as the difference between consecutive lower class limits or consecutive upper class limits.
Example 1: Constructing a Frequency Table The scores of 30 SS1 students in a General Mathematics test (out of 50) are: 35, 42, 28, 15, 30, 45, 22, 38, 25, 18, 40, 33, 29, 36, 20, 48, 31, 26, 39, 23, 17, 44, 32, 27, 34, 41, 19, 37, 21,
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6. Step 1: Find the range (Highest score - Lowest score). Range = 48 - 15 =
3
3. Step 2: Decide on the number of classes (usually 5-10) and an approximate class width. Let's choose 7 classes with a class width of
5. Starting from 15, classes could be 15-19, 20-24, etc.
Step 3: Tally the scores into the chosen classes. | Class Interval | Tally Marks | Frequency (f) | Class Boundaries | Class Mark (x) | | :------------- | :---------- | :-------------- | :--------------- | :------------- | | 15 - 19 | |||| | 5 | 14.5 - 19.5 | 17 | | 20 - 24 | |||| | 5 | 19.5 - 24.5 | 22 | | 25 - 29 | |||| || | 7 | 24.5 - 29.5 | 27 | | 30 - 34 | |||| || | 7 | 29.5 - 34.5 | 32 | | 35 - 39 | |||| | 5 | 34.5 - 39.5 | 37 | | 40 - 44 | |||| | 5 | 39.5 - 44.5 | 42 | | 45 - 49 | ||| | 3 | 44.5 - 49.5 | 47 | | Total | | 37 | | | Self-correction: Total frequency should be 30 based on the initial data. Let's re-tally carefully.
Scores: 35, 42, 28, 15, 30, 45, 22, 38, 25, 18, 40, 33, 29, 36, 20, 48, 31, 26, 39, 23, 17, 44, 32, 27, 34, 41, 19, 37, 21, 46. 15-19: 15, 18, 17, 19 (4 scores) 20-24: 22, 20, 23, 21 (4 scores) 25-29: 28, 25, 29, 26, 27 (5 scores) 30-34: 30, 33, 31, 32, 34 (5 scores) 35-39: 35, 38, 36, 39, 37 (5 scores) 40-44: 42, 40, 44, 41 (4 scores) 45-49: 45, 48, 46 (3 scores)
Revised Frequency Table: | Class Interval | Tally Marks | Frequency (f) | Class Boundaries | Class Mark (x) | | :------------- | :---------- | :-------------- | :--------------- | :------------- | | 15 - 19 | |||| | 4 | 14.5 - 19.5 | 17 | | 20 - 24 | |||| | 4 | 19.5 - 24.5 | 22 | | 25 - 29 | |||| | 5 | 24.5 - 29.5 | 27 | | 30 - 34 | |||| | 5 | 29.5 - 34.5 | 32 | | 35 - 39 | |||| | 5 | 34.5 - 39.5 | 37 | | 40
Public Health and Community Development: Data presentation is crucial for understanding health trends in Nigerian communities. For instance, a bar chart could show the number of reported cases of malaria in different local government areas (LGAs) in a state, helping health officials identify hotspots for intervention. A line graph could track the trend of vaccination rates for children over several years in a particular primary health care center, allowing health workers to assess the effectiveness of immunization campaigns. A pie chart could represent the proportion of different causes of death in a community, guiding resource allocation for disease prevention.
Economy and Market Research: Nigerian businesses constantly collect data to understand consumer behavior and market trends. A histogram could show the distribution of prices of a staple food item like a bag of rice across various markets in a city like Ibadan, indicating price variability and potential market inefficiencies. A bar chart could compare the sales figures of different brands of soft drinks (e.g., Coke, Pepsi, Fanta) in a specific quarter, informing marketing strategies. A line graph could track the stock prices of companies listed on the Nigerian Exchange Group (NGX) over a period, aiding investors in decision-making.
Education and Demographics: Educational institutions and government agencies use data presentation to plan and allocate resources. A frequency table can summarize JAMB scores for candidates aspiring for university admission, while a histogram can visualize the distribution of these scores, helping universities set cut-off marks. A pie chart could represent the distribution of students across different academic departments in a secondary school (Arts, Science, Commercial), guiding the allocation of teachers and resources. Similarly, a pie chart could show the ethnic or religious composition of a town during a census.