Data Collection and Sampling Notes

Edexcel GCSE Maths: Revision notes

Key facts

  • A population is everyone studied; a sample is a smaller group chosen from it.
  • A big sample can still be biased if it is not representative.
  • Pie chart angle =frequencytotal×360∘=\dfrac{\text{frequency}}{\text{total}}\times360^\circ.
  • A time series has time on the horizontal axis and shows trends.
  • A stem-and-leaf diagram keeps every value and needs a key; leaves go in order.

Samples and populations

Studying everyone is often impractical, so we study a sample and use it to estimate the population.

A population is the whole group; a sample is the part selected.

A random sample gives every member an equal chance of being chosen.

Larger, more representative samples give more reliable estimates. A poor or small sample is biased and can mislead.

  1. 1

    Population

    the whole group, too many to survey

  2. 2

    Select a random sample

    every member has an equal chance

  3. 3

    Collect data from the sample

    larger and more representative is better

  4. 4

    Estimate the population

    a biased sample misleads

From population to sample and back to an estimate.

Population

Meaning:
Everyone being studied
In practice:
Often too many to survey

Sample

Meaning:
A group taken from it
In practice:
Should represent the population

A school surveys 20 students from the canteen queue about lunch. What is the main problem?

Charts for categories

Frequency tables, bar charts, pie charts and pictograms all display categories and their counts.

Pie chart: each category is a sector with angle frequencytotal×360∘\dfrac{\text{frequency}}{\text{total}}\times360^\circ.

Bar charts have equal-width bars with gaps between them.

A pictogram needs a key that says what each symbol stands for.

0102030405060BlueRedGreenOtherColourFrequency
Illustrative values: 180 people choose a colour. Pie angles: blue 90°, red 120°, green 60°, other 90°.

Frequency table

  • Each category and its count

Bar chart

  • Bar height = frequency

Pie chart

  • Sector angle = share of 360°

Pictogram

  • Symbols with a key
  • Pie chart anglefrequencytotal×360∘\dfrac{\text{frequency}}{\text{total}}\times360^\circ

Worked example

45 of 180 people chose blue. Find the pie chart angle.

In a survey of 60 people, 15 chose tea. What is the angle for tea?

Time series graphs

A time series shows how a quantity changes over time, with time on the horizontal axis.

Points are joined by straight lines to show the pattern.

They are used to describe trends: a general upward or downward direction, or a seasonal pattern that repeats.

They are not used to read exact single values.

  1. 1

    Axes

    Time horizontal, quantity vertical

  2. 2

    Trend

    Upward, downward or steady

  3. 3

    Seasonal

    Repeating pattern?

  4. 4

    Odd values

    Any spikes or dips

Describing a time series

Trend

  • The general direction over the whole period

Seasonal

  • A pattern that repeats at regular intervals

A time series shows ice cream sales peaking every summer. This repeating pattern is called...

Stem-and-leaf diagrams

Each value is split into a stem and a leaf, so every data value stays visible.

The stem is the leading digits (here the tens); the leaf is the last digit.

Leaves go in ascending order and you must give a key: for example, "2 | 3 means 23".

A back-to-back diagram puts two data sets on either side of one stem, for easy comparison.

012341 (tens)2 (tens)3 (tens)StemNumber of values
Number of leaves on each stem for 12, 15, 18, 20, 23, 23, 29, 34, 36: the stem-and-leaf shape is a sideways bar chart.

Stem

Row 1:
1
Row 2:
2
Row 3:
3

Leaves

Row 1:
2 5 8
Row 2:
0 3 3 9
Row 3:
4 6

In the diagram, how many values are in the 20s?

Choosing the right diagram

The type of data decides the best diagram, and a poor choice can mislead.

Match the diagram to the data:

  • categories: bar chart, pie chart or pictogram
  • small sets of numbers: stem-and-leaf or frequency table
  • continuous data or data over time: histogram or time series
  • comparing two sets: back-to-back stem-and-leaf or dual bar chart
  1. 1

    Categories

    bar chart, pie chart or pictogram

  2. 2

    Small set of numbers

    stem-and-leaf or frequency table

  3. 3

    Continuous or over time

    histogram or time series

  4. 4

    Comparing two sets

    back-to-back stem-and-leaf or dual bar chart

Pick the diagram from the type of data.

Categorical

  • Bar chart, pie chart, pictogram

Discrete, small range

  • Stem-and-leaf, frequency table

Continuous or over time

  • Histogram, time series

Comparing two sets

  • Back-to-back stem-and-leaf, dual bar chart

Which is best for comparing two small sets of exam marks directly?

Try an exam question

60 students chose a favourite drink: 15 chose tea. (a) Work out the angle for tea on a pie chart. (b) Sara surveys 20 students from the canteen queue to find out about the whole school. Give one reason why her sample may not be representative.

[3 marks]

That's the notes covered.

Carry on to the next subtopic.