Charts and graphs

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수업 노트

Types of Data

Qualitative data describes qualities or categories, such as favourite colour or type of pet.
Discrete data can only take specific values, usually whole numbers, such as the number of siblings a student has.
Continuous data can take any value within a range, such as height or time, and is measured rather than counted.
Choosing the right chart depends on the type of data you have.

Tally Charts and Frequency Tables

A tally chart uses tally marks to record each occurrence of a value as data is collected.
Tally marks are grouped in fives for easy counting.
A frequency table shows each value or category and the number of times it occurs (its frequency).
Frequency tables make it easy to see the most and least common values.

Bar Charts and Pictograms

A bar chart uses rectangular bars with lengths proportional to the values they represent.
Bars can be drawn vertically or horizontally.
In a dual or composite bar chart, bars are grouped or stacked to compare two or more sets of data.
A pictogram uses pictures or symbols to represent data, with a key showing what each symbol stands for.
In a pictogram, part of a symbol can represent a fraction of the value.

Pie Charts

A pie chart shows data as slices of a circle, where each slice represents a proportion of the whole.
To find the angle for each slice, use the formula: angle = (frequency ÷ total frequency) × 360°.
All the angles in a pie chart add up to 360°.
Pie charts are best for showing percentages or proportions of different groups.

Line Graphs and Time Series

A line graph plots ordered observations as points connected by straight lines.
Line graphs are ideal for showing how data changes over time (a time series).
The x-axis usually shows time and the y-axis shows the variable being measured.
A line graph makes trends, such as increases or decreases, easy to spot.

Stem-and-Leaf Diagrams and Frequency Diagrams

A stem-and-leaf diagram splits each data value into a stem (usually the leading digit) and a leaf (usually the last digit).
Stem-and-leaf diagrams keep the original data values while showing the shape of the distribution.
A frequency diagram (or histogram) uses adjacent rectangles to show the frequency of data in intervals (bins).
In a histogram, the area of each bar is proportional to the frequency.

Choosing an Appropriate Chart

Use a pie chart to show proportions or percentages of a whole.
Use a bar chart to compare frequencies of different categories.
Use a line graph to show changes over time.
Use a scatter plot to show the relationship between two variables.
Use a stem-and-leaf diagram to display the shape of a small data set while keeping the original values.

Spotting Misleading Graphs

A misleading graph can distort data by using a y-axis that does not start at zero.
Unequal intervals on an axis can make differences look larger or smaller than they really are.
Pictures or 3D effects in pictograms and bar charts can exaggerate differences.
Always check the scale, labels, and starting point of a graph before drawing conclusions.

슬라이드

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연습 문제

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1.Which type of chart is best for showing how a quantity changes over a period of time, such as annual revenue from 1990 to 2000?
Easy
- APie chart
- BLine chart
- CStem-and-leaf diagram
- DPictogram
2.A pie chart is used to show percentage values. If one category is 25% of the total, what angle should its sector have?
Easy
- A25°
- B45°
- C90°
- D180°
3.The label on the x-axis of a chart reads 'Distance travelled (m)'. What does the '(m)' tell you?
Medium
- AThe maximum value on the axis
- BThe unit of the scale
- CThe number of data points
- DThe title of the chart
4.Which of the following are common elements of a chart? (select all that apply)
Medium
- ATitle
- BAxes with scales
- CLegend or key
- DGridlines
- ECalculator
5.A histogram consists of adjacent rectangles erected over discrete intervals, with area equal to frequency.
Easy
True or false?
6.Match each type of chart to its main use.
Medium
- Pie chart
- Line chart
- Bar chart
- Scatter plot
- Show parts of a whole as percentages
- Show change over time
- Compare frequencies of categories
- Show relationship between two variables
7.Put these steps for drawing a pie chart in the correct order.
Medium
- Calculate the total frequency
- Work out each category's fraction of the total
- Multiply each fraction by 360° to find the sector angle
- Draw and label the sectors
8.A bar chart showing test scores starts its vertical axis at 50 instead of 0. What effect does this have on the chart?
Hard
- AIt makes differences between bars look smaller
- BIt makes differences between bars look larger
- CIt does not change the appearance of the bars
- DIt changes the actual values of the data

더 많은 문제

9.Match each chart type to the feature that best describes it.
Medium
- Histogram
- Bar chart
- Pie chart
- Line chart
- Scatter plot
- Adjacent rectangles over discrete intervals, area equal to frequency
- Rectangular bars with lengths proportional to the values represented
- Shows percentage values as slices of a circle
- Ordered observations joined by lines
- Points for two variables not joined by lines
10.Put these stages of drawing a bar chart in the correct order.
Medium
- Draw and label the axes, choosing a suitable scale
- Collect the data and make a frequency table
- Draw bars of equal width with heights matching the frequencies
- Give the chart a title and add a key if needed
11.Which of the following are elements that a chart may typically include? (select all that apply)
Medium
- AA title above the main graphic
- BA legend or key when multiple variables appear
- CNumbered paragraphs explaining each bar
- DAxes with scales and labels
- EGridlines to aid visual alignment
12.Which of the following are types of data? (select all that apply)
Medium
- AQualitative
- BDiscrete
- CContinuous
- DHistogram
- EPie chart
13.A histogram consists of adjacent rectangles erected over discrete intervals. What does the area of each rectangle represent?
Medium
- AThe frequency of observations in that interval
- BThe total number of intervals
- CThe width of the interval
- DThe midpoint of the interval
14.Which type of chart shows percentage values as a slice of a pie?
Medium
- APie chart
- BBar chart
- CLine chart
- DScatter plot
15.A line chart is a two-dimensional scatterplot of ordered observations. How are the observations connected?
Medium
- AFollowing their order
- BBy size, largest to smallest
- CBy colour
- DThey are not connected
16.A scatter plot shows a relationship of two variables with dots or other symbols. How are the symbols connected?
Medium
- AThey are not connected by lines
- BThey are connected by straight lines
- CThey are connected by curved lines
- DThey are connected by dashed lines
17.A radar chart shows how a dependent variable, represented by distances from the centre of a circle, varies with respect to an independent variable. What is the independent variable?
Medium
- AThe radial location around the circle
- BThe distance from the centre
- CThe area of the circle
- DThe colour of the points
18.A bubble chart is a two-dimensional scatterplot where a third variable is represented by what?
Medium
- AThe size of the points
- BThe colour of the points
- CThe shape of the points
- DThe position of the points
19.A pie chart shows the favourite sports of 120 students. If 45 students chose football, what is the angle of the football sector?
Medium
- A135°
- B120°
- C150°
- D108°
20.Data that presents percentages in different groups (such as 'satisfied, not satisfied, unsure') is often displayed in a pie chart. Which other chart type might make it more easily understood?
Medium
- AHorizontal bar chart
- BLine chart
- CScatter plot
- DHistogram
21.A chart uses a horizontal and a vertical axis. What are they usually referred to as?
Medium
- Ax-axis and y-axis
- Ba-axis and b-axis
- Chorizontal axis and vertical axis only
- Dmajor axis and minor axis
22.Within a graph, a grid of lines may appear to aid in the visual alignment of data. What are the emphasized lines called?
Medium
- AMajor gridlines
- BMinor gridlines
- CAxis lines
- DTrendlines
23.A tally chart records the colours of 20 cars. Which type of data is being recorded?
Easy
- AQualitative data
- BDiscrete data
- CContinuous data
- DQuantitative data
24.A survey records the number of pets owned by each student. Which type of data is this?
Medium
- ADiscrete data
- BContinuous data
- CQualitative data
- DCategorical data
25.A stopwatch records the time taken for 30 students to run 100 m. Which type of data is this?
Medium
- AContinuous data
- BDiscrete data
- CQualitative data
- DCategorical data
26.A tally chart is used to record the frequency of each category before drawing a bar chart.
Easy
True or false?
27.A pie chart shows how 240 students travel to school. If 60 students walk, what is the angle of the walking sector?
Medium
- A90°
- B60°
- C120°
- D45°
28.A bar chart has a vertical axis starting at 50 instead of 0. What effect does this have?
Medium
- AIt makes small differences between bars look larger than they really are.
- BIt makes the bars appear shorter than they really are.
- CIt changes the total frequency of the data.
- DIt makes the chart impossible to read.
29.A pie chart shows how 300 students travel to school. 120 students walk, 90 cycle and the rest take the bus. What is the angle of the bus sector?
Medium
- A108°
- B90°
- C120°
- D144°
30.A bar chart shows the number of books read by 5 students. The bar for Amara reads 12 and the bar for Ben reads 8. How many more books did Amara read than Ben?
Medium
- A4
- B20
- C6
- D8
31.A graph of a car journey has a vertical axis labelled 'Speed (m/s)' and a horizontal axis labelled 'Time (s)'. Which of the following statements must be true? (select all that apply)
Medium
- AThe vertical axis shows speed measured in metres per second.
- BThe horizontal axis shows time measured in seconds.
- CThe graph shows distance in metres.
- DThe graph shows acceleration in m/s².
- EThe vertical axis shows time measured in seconds.
32.The label on the horizontal axis of a graph reads 'Distance travelled (m)'. What does the '(m)' tell you?
Medium
- AThe distance is measured in metres.
- BThe distance is measured in minutes.
- CThe graph shows mass.
- DThe graph shows miles.
33.A pie chart shows how a family spends £1800 each month. If £450 is spent on rent, what is the angle of the rent sector?
Medium
- A90°
- B45°
- C60°
- D120°
34.A line graph shows a company's annual revenue from 1990 to 2000. The revenue in 1995 was £3.2 million and in 2000 it was £4.8 million. By how much did the revenue increase?
Medium
- A£1.6 million
- B£1.4 million
- C£8.0 million
- D£1.2 million
35.A pie chart can be used to show how a single quantity changes over a period of time.
Medium
True or false?
36.Match each chart type to its main use.
Medium
- Line chart
- Pie chart
- Bar chart
- Histogram
- Showing change over time
- Showing parts of a whole
- Comparing categories
- Showing the frequency of continuous data
37.A histogram has bins of width 4, 4, 8 and 8. The first two rectangles have heights 5 and 3. What is the frequency of the bin of width 4 with height 5?
Medium
- A20
- B9
- C5
- D80
38.A tally chart can be used to record the frequency of each category before drawing a bar chart.
Easy
True or false?
39.A line graph shows the temperature at noon over five days: 12°C, 15°C, 11°C, 18°C and 14°C. On which day was the temperature highest?
Medium
- ADay 4
- BDay 2
- CDay 5
- DDay 1
40.A pie chart shows how 120 students travel to school. 30 students walk, 45 cycle and the rest take the bus. What is the angle of the bus sector?
Medium
- A135°
- B90°
- C45°
- D120°
41.A pie chart shows the favourite sports of 120 students. If 45 students chose football, what is the angle of the football sector? Give your answer in degrees.
Medium
42.Complete the sentences about types of data.
Medium
Data that can only take particular values, such as the number of pets, is called ____ data. Data that can take any value in a range, such as height, is called ____ data.
43.Complete the sentence about the label on a chart axis.
Easy
If the scale is numerical, the label is often suffixed with the ____ of that scale in parentheses.
44.A pie chart is used to show percentage values. If one category is 25% of the total, what angle should its sector have? Give your answer in degrees.
Medium
45.A pie chart shows the favourite colours of 60 students. If 15 students chose blue, what is the angle of the blue sector? Give your answer in degrees.
Medium
46.A pie chart shows how 200 students travel to school. If 50 students cycle, what angle should the cycling sector have? Give your answer in degrees.
Medium
47.Complete the sentence about a chart axis label.
Easy
The label 'Distance travelled (m)' tells you that the distance is measured in ____.
48.What name is given to the emphasized lines in the grid of a graph that help with alignment of data?
Easy
49.A pie chart shows the favourite drinks of 90 students. If 18 students chose water, what angle should the water sector have? Give your answer in degrees.
Medium
50.A pie chart shows how a family spends £1200 each month. If £300 is spent on food, what angle should the food sector have? Give your answer in degrees.
Hard
51.Complete the sentence about a chart title.
Easy
A graph's title usually appears ____ the main graphic and provides a succinct description of what the data in the graph refers to.
52.A pie chart shows the favourite subjects of 150 students. If 30 students chose art, what angle should the art sector have? Give your answer in degrees.
Medium
53.Explain why a line chart is often a better choice than a pie chart for showing annual revenue from 1990 to 2000.
Medium
54.Explain why a pie chart is often used to show data that presents percentages in different groups, such as 'satisfied, not satisfied, unsure'.
Hard
55.Explain why a line chart is often a better choice than a bar chart for showing annual revenue from 1990 to 2000.
Hard
56.A pie chart shows the favourite sports of 120 students. If 45 students chose football, what is the angle of the football sector? Give your answer in degrees.
Medium
- A149 °
- B163 °
- C121 °
- D135 °
57.A pie chart is used to show percentage values. If one category is 25% of the total, what angle should its sector have? Give your answer in degrees.
Medium
- A108 °
- B99 °
- C81 °
- D90 °
58.A pie chart shows the favourite colours of 60 students. If 15 students chose blue, what is the angle of the blue sector? Give your answer in degrees.
Medium
- A108 °
- B90 °
- C99 °
- D81 °
59.A pie chart shows how 200 students travel to school. If 50 students cycle, what angle should the cycling sector have? Give your answer in degrees.
Medium
- A81°
- B108°
- C99°
- D90°
60.A pie chart shows the favourite drinks of 90 students. If 18 students chose water, what angle should the water sector have? Give your answer in degrees.
Medium
- A65°
- B79°
- C86°
- D72°
61.A pie chart shows how a family spends £1200 each month. If £300 is spent on food, what angle should the food sector have? Give your answer in degrees.
Hard
- A90°
- B99°
- C81°
- D108°
62.A pie chart shows the favourite subjects of 150 students. If 30 students chose art, what angle should the art sector have? Give your answer in degrees.
Medium
- A79°
- B65°
- C86°
- D72°

복습 노트

## Charts and Graphs — KS3 Statistics Revision **Why charts?** Charts (graphs) show data with symbols — bars, lines, slices. They are read faster than raw data and reveal relationships between parts of the data. They can be drawn by hand or by computer. ## Types of data - **Qualitative** — categories (e.g. colour, satisfied/unsure). - **Discrete** — counted values (e.g. number of pets). - **Continuous** — measured values (e.g. height, time). ## Tables - **Tally chart** — counts recorded in groups of five. - **Frequency table** — lists each value or group with its frequency. ## Common charts - **Bar chart** — rectangular bars with lengths proportional to the values; bars can be vertical or horizontal. - **Dual / composite bar chart** — bars for two or more groups shown side by side or stacked. - **Pictogram** — pictures or symbols stand for a fixed number of items. - **Pie chart** — shows percentage values as slices of a pie. Angle of a slice = (frequency ÷ total) × 360°. - **Line chart / time series** — ordered observations joined in order; good for numbers changing over time. - **Stem-and-leaf diagram** — splits each value into a stem and a leaf, keeping the original data. - **Frequency diagram / histogram** — tabular frequencies shown as adjacent rectangles over discrete intervals (bins); the area of each rectangle equals the frequency of that interval. - **Scatter plot** — shows the relationship between two variables with unconnected dots; a trendline may be added. ## Parts of a chart - **Title** — above the graphic; says what the data refers to. - **Axes** — horizontal x-axis and vertical y-axis, each with a **scale** (graduations) and a **label**. A numerical label often ends with the unit in brackets, e.g. "Distance travelled (m)". - **Gridlines** — major gridlines mark regular or significant graduations; minor gridlines fill the gaps. - **Legend (key)** — lists each variable and shows how it appears, so data can be identified. ## Choosing a chart - Percentages in groups → pie chart, or a horizontal bar chart for easier reading. - Numbers changing over time → line chart. - Relationship between two variables → scatter plot. ## Misleading graphs — watch for - A y-axis that does not start at zero. - Uneven or broken scales. - Missing labels, units or key. - Pictures drawn at different sizes in a pictogram. **Exam tip:** always read the title, axes, scale and key before answering.

Chart (graph): A graphical representation of data in which the data is shown by symbols, such as bars in a bar chart, lines in a line chart, or slices in a pie chart.
Qualitative data: Data that describes a quality or category rather than a number.
Discrete data: Data that can only take particular values, usually counts.
Continuous data: Data that can take any value within a range, usually measurements.
Tally chart: A table used to record counts, with tallies grouped in fives.
Frequency table: A table showing each value or group together with its frequency.
Bar chart: A chart with rectangular bars whose lengths are proportional to the values they represent; bars may be vertical or horizontal.
Pictogram: A chart in which pictures or symbols represent a fixed number of items.
Pie chart: A chart showing percentage values as slices of a pie; the angle of a slice is (frequency ÷ total) × 360°.
Line chart (time series): A two-dimensional scatterplot of ordered observations where the points are connected in order; used for values changing over time.
Stem-and-leaf diagram: A diagram that splits each value into a stem and a leaf, keeping the original data visible.
Histogram (frequency diagram): Tabular frequencies shown as adjacent rectangles over discrete intervals (bins), with area equal to the frequency of the observations in the interval.
Scatter plot: A chart showing the relationship between two variables with dots or symbols that are not connected by lines; a trendline may be added.
Axis (x-axis, y-axis): A dimension of the data shown on a chart; the horizontal axis is the x-axis and the vertical axis is the y-axis.
Scale: The periodic graduations on an axis, usually with numerical or categorical indications.
Axis label: Text beside or outside an axis briefly describing the dimension; a numerical label often ends with the unit in brackets, e.g. "Distance travelled (m)".
Gridlines: Lines within a graph that aid visual alignment of data; major gridlines mark regular or significant graduations and minor gridlines fill the remainder.
Legend (key): A list of the variables in a chart with an example of how each appears, so the data for each variable can be identified.
Title: A succinct description above the main graphic saying what the data in the graph refers to.

플래시카드

What is a chart (or graph)?

A graphical representation for data and information visualisation, in which the data is represented by symbols such as bars, lines or slices.

Why are charts often used instead of raw data tables?

Charts ease understanding of large quantities of data and the relationships between parts of the data, and can usually be read more quickly than raw data.

What is qualitative data?

Data that describes qualities or categories rather than numbers, such as eye colour or favourite subject.

What is discrete data?

Numerical data that can only take particular separate values, usually whole numbers counted in jumps, such as the number of pets in a household.

What is continuous data?

Numerical data that can take any value within a range, such as height or time, measured rather than counted.

What is a tally chart used for?

To record how often each value or category occurs by making tally marks in groups, usually of five, before totalling them into a frequency.

What is a frequency table?

A table that lists each value or category alongside the number of times it occurs (its frequency).

What does a bar chart show?

A chart with rectangular bars whose lengths are proportional to the values they represent; the bars can be plotted vertically or horizontally.

What is a dual or composite bar chart?

A bar chart that shows two or more sets of data side by side or stacked within the same categories, so the groups can be compared.

What is a pictogram?

A chart that uses pictures or symbols to represent data, where each symbol stands for a fixed number of items, shown in a key.

What does a pie chart show?

Percentage values as slices of a pie; each slice represents a category's share of the whole.

How do you calculate the angle of a pie chart slice?

Angle = (frequency ÷ total frequency) × 360°.

What is a line chart used for?

A two-dimensional scatterplot of ordered observations where the points are connected in order, often used to show how a value changes over time.

What is a time series?

Data recorded at regular intervals over time, usually displayed on a line graph so trends can be seen.

What is a stem-and-leaf diagram?

A diagram that splits each data value into a stem (the leading digit or digits) and a leaf (the final digit), keeping the original values visible while showing the shape of the data.

What is a frequency diagram?

A graph that shows frequencies, such as a histogram, with adjacent rectangles over discrete intervals whose area equals the frequency in each interval.

What is a histogram?

A chart of tabular frequencies shown as adjacent rectangles over discrete intervals (bins), with an area equal to the frequency of the observations in the interval.

What is a scatter plot?

A chart showing the relationship between two variables with dots or symbols that are not connected by lines; a trendline may be added to show trends.

What is a legend (or key) on a chart?

A list of the variables appearing in the chart with an example of their appearance, allowing the data from each variable to be identified.

What is the title of a graph and where does it usually appear?

A succinct description of what the data in the graph refers to; it usually appears above the main graphic.

What are the x-axis and y-axis?

The horizontal axis is the x-axis and the vertical axis is the y-axis; each has a scale and usually a label describing the dimension represented.

What are major and minor gridlines?

A grid of lines that aids visual alignment of data; emphasised lines at regular or significant graduations are major gridlines, and the remainder are minor gridlines.

Which chart is often best for showing percentages in different groups?

A pie chart is often used, but the data may be more easily understood when presented in a horizontal bar chart.

Which chart is often best for showing numbers that change over a period of time?

A line chart, because it shows how the value changes over time.

How can a graph be misleading?

By using a scale that does not start at zero, uneven intervals, or a misleading choice of chart type, which can exaggerate or hide differences in the data.

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