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GCSEMathsAQAHigherFlashcards6. StatisticsCumulative Frequency & Box Plots

Cumulative Frequency & Box Plots (AQA GCSE Maths)

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    What is meant by cumulative frequency?

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  • What is meant by cumulative frequency?

    The cumulative frequency of an item is the total frequency of all items that are less than or equal to the given item.

    Cumulative frequency is a running total of the frequencies.

  • In a cumulative frequency table, such as the one below, how do you find the actual frequency for a particular group?

    Group

    Cumulative frequency

    0 ≤ x < 20

    14

    0 ≤ x < 40

    39

    0 ≤ x < 60

    68

    To find the actual frequency for a particular group from a cumulative frequency table, subtract the previous cumulative frequency from the cumulative frequency for the the group that you want.

    Group

    Cumulative Frequency

    Actual frequency

    0 ≤ x < 20

    14

    14

    0 ≤ x < 40

    39

    39 - 14 = 25

    0 ≤ x < 60

    68

    68 - 39 = 29

  • How do you draw a cumulative frequency diagram?

    To draw a cumulative frequency diagram:

    • For each group, plot the cumulative frequency at the endpoint of the group

    • Join the points together with a smooth curve that is always increasing

  • True or False?

    To draw a cumulative frequency diagram, you plot the midpoint of a group against its frequency.

    False.

    To draw a cumulative frequency diagram, you do not plot the midpoint of a group against its frequency. This is a mistake that students often make on the exam.

    You plot the endpoint of a group against its cumulative frequency.

  • What shape does a typical cumulative frequency diagram make?

    A typical cumulative frequency diagram is an 's-shaped' curve, e.g.

    An example of a typical 's-shaped' curve of a cumulative frequency diagram.

  • True or False?

    A cumulative frequency diagram will get slightly closer to the x-axis again at the end of the curve.

    False.

    A cumulative frequency diagram will never get closer to the x-axis.

  • If the total frequency is 100, how do you use a cumulative frequency diagram to estimate the median value?

    If the total frequency is 100, you can use a cumulative frequency diagram to estimate the median value.

    1. Draw a horizontal line from 50 (100 divided by 2) on the vertical axis to the curve.

    2. Draw a vertical line down from this point on the curve to the horizontal axis.

    The value on the horizontal axis is an estimate of the median.

  • How can you estimate the lower quartile using a cumulative frequency diagram?

    To estimate the lower quartile using a cumulative frequency diagram:

    1. Divide the total frequency by 4.

    2. Draw a horizontal line from that result on the vertical axis to the curve.

    3. Draw a vertical line down from this point to the horizontal axis.

    The number on the horizontal axis is an estimate for the lower quartile.

  • True or False?

    To find the number of data items that are greater than a particular value:

    • find the relevant value on the x-axis,

    • draw a vertical line up to the curve,

    • then draw a horizontal line back across to the y-axis.

    The value on the y-axis will be the number of data items that are greater than that value.

    False.

    If you follow those steps you have found the number of data items that are less than or equal to the specified value.

    To find the number of data items that are greater than the value, you need to subtract the number of data items that are less than or equal to the specified value from the total number of data items.

  • What are the five values needed to draw a box plot?

    The five values needed to draw a box plot are: lowest data value, lower quartile, median, upper quartile, and highest data value.

  • What proportion of the data set does the box in a box plot represent?

    The box in a box plot represents the middle 50% of the data set.

  • What is the measure represented by the box in a box plot?

    The measure represented by the box in a box plot is the interquartile range (IQR).

  • What do the "whiskers" in a box plot represent?

    The whiskers represent the lowest 25% and the highest 25% of the data.

  • True or False?

    The median line in a box plot is always in the middle of the box.

    False.

    The median line in a box plot is not always in the middle of the box.

  • What does a smaller interquartile range (IQR) indicate when comparing box plots?

    A smaller IQR indicates that the data is more consistent or less spread out.

Previous:HistogramsNext:Scatter Graphs & Correlation

    1. Topic 1

      Number Operations

    2. Topic 2

      Prime Factors, HCF & LCM

    3. Topic 3

      Powers, Roots & Standard Form

    4. Topic 4

      Fractions

    5. Topic 5

      Percentages

    6. Topic 6

      Simple & Compound Interest, Growth & Decay

    7. Topic 7

      Fractions, Decimals & Percentages

    8. Topic 8

      Rounding, Estimation & Bounds

    9. Topic 9

      Surds

    10. Topic 10

      Using a Calculator

    1. Topic 1

      Introduction to Algebra

    2. Topic 2

      Algebraic Roots & Indices

    3. Topic 3

      Expanding Brackets

    4. Topic 4

      Factorising

    5. Topic 5

      Completing the Square

    6. Topic 6

      Algebraic Fractions

    7. Topic 7

      Rearranging Formulas

    8. Topic 8

      Algebraic Proof

    9. Topic 9

      Linear Equations

    10. Topic 10

      Quadratic Equations

    11. Topic 11

      Simultaneous Equations

    12. Topic 12

      Iteration

    13. Topic 13

      Forming & Solving Equations

    14. Topic 14

      Functions

    15. Topic 15

      Coordinate Geometry

    16. Topic 16

      Linear Graphs

    17. Topic 17

      Graphs of Functions

    18. Topic 18

      Equation of a Circle

    19. Topic 19

      Estimating Gradients & Areas under Graphs

    20. Topic 20

      Real-Life Graphs

    21. Topic 21

      Solving Inequalities

    22. Topic 22

      Graphing Inequalities

    23. Topic 23

      Transformations of Graphs

    24. Topic 24

      Sequences

    1. Topic 1

      Ratios

    2. Topic 2

      Problem Solving with Ratios

    3. Topic 3

      Direct & Inverse Proportion

    4. Topic 4

      Standard & Compound Units

    5. Topic 5

      Exchange Rates & Best Buys

    1. Topic 1

      Symmetry & Shapes

    2. Topic 2

      Angles in Polygons & Parallel Lines

    3. Topic 3

      Bearings, Scale Drawing, Constructions & Loci

    4. Topic 4

      Circle Theorems

    5. Topic 5

      Area & Perimeter

    6. Topic 6

      Circles, Arcs & Sectors

    7. Topic 7

      Volume & Surface Area

    8. Topic 8

      Congruence, Similarity & Geometrical Proof

    9. Topic 9

      Area & Volume of Similar Shapes

    10. Topic 10

      Pythagoras & Trigonometry

    11. Topic 11

      Sine, Cosine Rule & Area of Triangles

    12. Topic 12

      3D Pythagoras & Trigonometry

    13. Topic 13

      Vectors

    14. Topic 14

      Transformations

    1. Topic 1

      Introduction to Probability

    2. Topic 2

      Simple Probability Diagrams

    3. Topic 3

      Tree Diagrams

    4. Topic 4

      Combined & Conditional Probability

    1. Topic 1

      Averages, Ranges & Data

    2. Topic 2

      Statistical Diagrams

    3. Topic 3

      Histograms

    4. Topic 4

      Cumulative Frequency & Box Plots

    5. Topic 5

      Scatter Graphs & Correlation