VidaaraPlay
Door 16 · Grade 8

📊 Data Representation

Data is collected information used for analysis

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Collection of Data and Frequency Tables

What is Data?

Data is a collection of facts, numbers, or information gathered for analysis. Examples include test scores, heights of students, number of pets in a family, or daily temperatures.

Types of Data:

TypeDefinitionExample
Primary DataCollected directly by the userConducting a survey in your class
Secondary DataTaken from already published sourcesUsing census data from a website

Collection of Data:

Data can be collected through:

• Surveys - Asking questions to people

• Experiments - Conducting tests

• Observations - Watching and recording

• Questionnaires - Written forms to fill out

• Interviews - One-on-one questioning

What is a Frequency Table?

A frequency table organizes data by showing how many times each value (or range of values) occurs. The number of times a value appears is called its frequency.

Steps to Create a Frequency Table:

• List…

Worked example

Problem: The marks obtained by 20 students in a maths test (out of 10) are: 7, 8, 6, 7, 9, 7, 8, 6, 7, 8, 9, 7, 6, 8, 7, 9, 7, 8, 6, 7. Prepare a frequency table.

  1. Step 1: Identify distinct values: 6, 7, 8, 9
  2. Step 2: Count occurrences using tally marks
  3. Step 3: Marks 6: appears 4 times → ||||
  4. Step 4: Marks 7: appears 8 times → |||| ||||
  5. Step 5: Marks 8: appears 5 times → |||| |

Answer: Step 5: Marks 8: appears 5 times → |||| |

Bar Graphs and Histograms

What is a Bar Graph?

A bar graph (or bar chart) is a visual representation of data using rectangular bars of different heights. The height of each bar represents the frequency of that category.

Features of a Bar Graph:

• X-axis (horizontal): Categories (e.g., colors, subjects, months)

• Y-axis (vertical): Frequency or values

• Bars: Separate rectangles with gaps between them

• Title: Describes what the graph shows

• Labels: Name the axes and categories

What is a Histogram?

A histogram is similar to a bar graph but is used for continuous data grouped into class intervals. In a histogram, bars touch each other (no gaps) because the data is continuous.

Bar Graph vs Histogram:

FeatureBar GraphHistogram
Data typeCategorical/discreteContinuous
Bar spacingGaps between barsBars touch each other
X-axisCategories (no order)Number line (ordered)
ExampleFavorite…

Worked example

Problem: The following data shows the number of students in different clubs: Music: 25, Sports: 40, Art: 30, Drama: 20, Science: 35. Draw a bar graph to represent this data.

  1. Step 1: Draw X-axis and Y-axis
  2. Step 2: Label X-axis as "Clubs", Y-axis as "Number of Students"
  3. Step 3: Choose scale: 1 unit = 5 students (up to 45)
  4. Step 4: Mark clubs: Music, Sports, Art, Drama, Science
  5. Step 5: Draw bars of heights: Music=25 (5 units), Sports=40 (8 units), Art=30 (6 units), Drama=20 (4 units), Science=35 (7 units)

Answer: Step 5: Draw bars of heights: Music=25 (5 units), Sports=40 (8 units), Art=30 (6 units), Drama=20 (4 units), Science=35 (7 units)

Pie Charts, Line Graphs, and Stem-and-Leaf Plots

What is a Pie Chart?

A pie chart (or circle graph) is a circular chart divided into sectors (slices). Each sector represents a proportion of the whole data set. The entire circle represents 100% or the total frequency.

Calculating Pie Chart Angles:

Each sector's angle = \(Category FrequencyTotal Frequency × 360°\)

What is a Line Graph?

A line graph shows data points connected by straight lines. It is ideal for showing trends over time or continuous change.

Features of Line Graph:

• X-axis usually shows time (years, months, days)

• Y-axis shows measured quantity

• Points are plotted and connected

• Multiple lines can compare different data sets

What is a Stem-and-Leaf Plot?

A stem-and-leaf plot is a way to organize data that shows both the shape of the distribution and the actual data values. The "stem" is the leading digit(s), and the "leaf" is the last…

Worked example

Problem: In a survey of 40 people about their preferred mode of transport: Car: 16, Bus: 12, Bicycle: 8, Walk: 4. Draw a pie chart. Find the angle for each sector.

  1. Step 1: Total = 16 + 12 + 8 + 4 = 40
  2. Step 2: Car angle = (16/40) × 360° = 0.4 × 360° = 144°
  3. Step 3: Bus angle = (12/40) × 360° = 0.3 × 360° = 108°
  4. Step 4: Bicycle angle = (8/40) × 360° = 0.2 × 360° = 72°
  5. Step 5: Walk angle = (4/40) × 360° = 0.1 × 360° = 36°

Answer: Step 5: Walk angle = (4/40) × 360° = 0.1 × 360° = 36°