Introduction to Charts & Co-ordinates
Charts and graphs are visual ways to represent data, making it easier to understand patterns, trends, and comparisons. Co-ordinates help us specify exact locations on a grid or map. These are fundamental skills in Functional Skills Maths Level 2, used in various real-life contexts from analysing survey results to reading maps.
This page will cover common chart types like pie charts, bar charts, line graphs, scatter diagrams, and pictographs, as well as how to use co-ordinates.
Pie Charts
A pie chart is a circular chart divided into sectors, illustrating numerical proportion. Each sector's angle is proportional to the quantity it represents.
- The whole circle represents 100% of the data (or the total amount).
- The whole circle is 360°.
Calculating the Angle for a Sector:
To find the angle needed for each sector in a pie chart, you first need to know the value (or frequency) for that sector and the total value (or total frequency) for all sectors.
The formula is:
Value for Sector Total Value × 360° = Angle for Sector
This works because you are finding what fraction of the total the sector represents, and then finding that same fraction of the total degrees in a circle (360°).
Calculating the Percentage for a Sector:
Similarly, to find the percentage for a sector:
Value for Sector Total Value × 100% = Percentage for Sector
A simple pie chart showing three categories.
Worked Example: Calculating Sector Angles
In a survey, 60 people were asked their favourite fruit. The results were: Apples (30), Bananas (15), Oranges (10), Grapes (5). Calculate the angle for each sector if this data was shown on a pie chart.
Total people surveyed = 30 + 15 + 10 + 5 = 60 people.
- Apples:
(30 / 60) × 360° = 0.5 × 360° = 180° - Bananas:
(15 / 60) × 360° = 0.25 × 360° = 90° - Oranges:
(10 / 60) × 360° = (1/6) × 360° = 60° - Grapes:
(5 / 60) × 360° = (1/12) × 360° = 30°
Check: The angles should add up to 360°. 180° + 90° + 60° + 30° = 360°. Correct!
Pie chart showing favourite fruits based on the example.
Bar Charts
A bar chart (or bar graph) uses rectangular bars with lengths proportional to the values they represent. Bars can be horizontal or vertical.
- Used for comparing discrete categories of data.
- Must have a clear title and labelled axes.
- The scale on the frequency axis must be consistent.
- Bars should be of equal width and have equal gaps between them (unless it's a histogram).
- Dual bar charts compare two sets of data for the same categories.
- Composite (or stacked) bar charts show how a total is divided into parts for each category.
A simple vertical bar chart.
Line Graphs
A line graph displays data as a series of points connected by straight line segments. They are often used to show trends or changes over time (continuous data).
- Both axes must be labelled clearly with appropriate scales.
- Points are plotted according to the data and then joined with straight lines.
- Useful for showing increases, decreases, or fluctuations.
A line graph showing a trend over four months.
Scatter Diagrams (Scatter Graphs)
A scatter diagram (or scatter graph) is used to show the relationship between two sets of numerical data. Each point on the graph represents one pair of data values.
- Helps to identify if there is a correlation (relationship) between the two variables.
- Positive correlation: As one variable increases, the other tends to increase (points generally slope upwards).
- Negative correlation: As one variable increases, the other tends to decrease (points generally slope downwards).
- No correlation: Points are scattered randomly, no clear relationship.
- A line of best fit can sometimes be drawn through the points to show the general trend (especially for positive or negative correlation). This line should follow the trend of the points with roughly an equal number of points above and below it.
A scatter diagram showing positive correlation with a line of best fit.
Pictographs (Pictograms)
A pictograph (or pictogram) uses pictures or symbols to represent data. Each symbol stands for a certain number of items.
- A key is essential to understand what each symbol represents.
- Parts of symbols can be used to show parts of the value (e.g., half a symbol).
- Good for a simple visual representation, especially for younger audiences or quick comparisons.
A pictograph showing apples sold, with a key.
Co-ordinates
Co-ordinates are pairs of numbers that define the position of a point on a grid, known as the Cartesian plane. They are written as (x, y).
- The first number is the x-coordinate (horizontal position - "along the corridor").
- The second number is the y-coordinate (vertical position - "up/down the stairs").
- The point (0,0) is called the origin.
- The horizontal line is the x-axis, and the vertical line is the y-axis.
Co-ordinate grid showing points P (2,3) and Q (-1,1).
Worked Examples: Charts & Co-ordinates
Example 1: Interpreting a Pie Chart
A survey of 120 students asked their favourite sport. The pie chart shows 90° for Football. How many students chose Football?
- The whole pie chart is 360°.
- Fraction for Football =
Angle for Football / Total Angle = 90° / 360° = 1/4. - Number of students who chose Football = Fraction × Total Students =
(1/4) × 120 = 30students.
Answer: 30 students chose Football.
Example 2: Reading a Bar Chart
A bar chart shows the number of pets owned by students: Dogs (15), Cats (20), Fish (10), Hamsters (5). Which pet is most popular, and how many more students own Cats than Hamsters?
- Most popular pet: Look for the tallest bar. Cats (20).
- Difference between Cats and Hamsters:
20 (Cats) - 5 (Hamsters) = 15.
Answer: Cats are most popular. 15 more students own Cats than Hamsters.
Example 3: Plotting Co-ordinates
Plot the points A(1, 2), B(-3, 1), and C(2, -2) on a co-ordinate grid. Describe the shape formed if you join A to B, B to C, and C to A.
(Imagine a grid here for plotting)
- For A(1,2): Start at origin, go 1 unit right (x-axis), then 2 units up (y-axis).
- For B(-3,1): Start at origin, go 3 units left (x-axis), then 1 unit up (y-axis).
- For C(2,-2): Start at origin, go 2 units right (x-axis), then 2 units down (y-axis).
- Joining A to B, B to C, and C to A forms a triangle.
Answer: The points form a triangle.
Test Your Chart & Co-ordinate Skills!
1. In a pie chart representing 60 people, how many degrees would represent 15 people?
Answer: 90°
Explanation: (15 / 60) × 360° = (1/4) × 360° = 90°.
2. A bar chart shows sales: Mon (£50), Tue (£70), Wed (£40). What were the total sales for these three days?
Answer: £160
Explanation: £50 + £70 + £40 = £160.
3. A line graph shows temperature. If it starts at 10°C and rises to 18°C, what is the increase?
Answer: 8°C
Explanation: 18°C - 10°C = 8°C.
4. In a pictograph, one car symbol represents 5 cars. How many symbols are needed for 25 cars?
Answer: 5 symbols
Explanation: 25 cars ÷ 5 cars/symbol = 5 symbols.
5. What are the co-ordinates of the origin on a grid?
Answer: (0,0)
Exam-Style Problems: Charts & Co-ordinates
1. A survey asked 200 people their favourite type of holiday. 40% chose Beach, 25% chose City Break, 15% chose Adventure, and the rest chose Cruise.
a) How many people chose Cruise?
b) Calculate the angle for the Beach sector on a pie chart.
Answers:
a) 40 people
b) 144°
Explanation:
- a) Percentage for Cruise = 100% - (40% + 25% + 15%) = 100% - 80% = 20%.
Number for Cruise = 20% of 200 = 0.20 × 200 = 40 people. - b) Angle for Beach = 40% of 360° = 0.40 × 360° = 144°.
2. The points P(2,5), Q(6,5), R(6,1) and S(2,1) are plotted on a grid. What shape is formed by joining P-Q-R-S-P?
Answer: A rectangle (specifically, a square in this case).
Explanation: Length PQ (horizontal) = 6-2 = 4 units. Length QR (vertical) = 5-1 = 4 units. Length RS (horizontal) = 6-2 = 4 units. Length SP (vertical) = 5-1 = 4 units. All sides are 4 units long, and adjacent sides are perpendicular (horizontal/vertical lines), forming a square. A square is a special type of rectangle.
Key Takeaways for Charts & Co-ordinates
- Pie Charts: Show proportions. Whole circle = 360° = 100%. Sector angle = (frequency/total) × 360°.
- Bar Charts: Compare discrete categories. Ensure labelled axes, consistent scale, and equal bar widths/gaps.
- Line Graphs: Show trends over time (continuous data). Plot points accurately and join with straight lines.
- Scatter Diagrams: Show relationships between two variables. Identify positive, negative, or no correlation. A line of best fit shows the general trend.
- Pictographs: Use symbols to represent data. Always include a key.
- Co-ordinates: Written as (x, y). X is horizontal ("along the corridor"), Y is vertical ("up/down the stairs"). Origin is (0,0).