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GCSEMathsAQAHigherFlashcards6. StatisticsHistograms

Histograms (AQA GCSE Maths)

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  • FrontFrequency Density

    State the formula for frequency density.

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  • State the formula for frequency density.

    The formula for frequency density is:  

    frequency space density equals fraction numerator frequency over denominator class space width end fraction.

  • When calculating frequency densities, given a table with a first column for the class intervals and a second column for the frequencies, it is useful to add two more columns to the table.

    What information should these columns be used for?

    Speed, s (km/h)

    Frequency

    .........

    .........

    20 less or equal than s less than 40

    5

    40 less or equal than s less than 50

    15

    When calculating frequency densities, given a table with a first column for the class intervals and a second column for the frequencies, two extra two columns should be added for class width and frequency density.

    Speed, s (km/h)

    Frequency

    Class width

    Frequency Density

    20 less or equal than s less than 40

    5

    20

    0.25

    40 less or equal than s less than 50

    15

    10

    1.5

  • True or False?

    A histogram is used to show the frequency distribution of discrete data.

    False.

    A histogram is used to show the frequency distribution of continuous data.

  • True or False?

    A histogram is the same as a bar chart but without the gaps between the bars.

    False.

    A histogram is not the same as a bar chart.

    A histogram uses frequency density, whereas a bar chart uses frequency.

  • What type of statistical diagram is shown below.

    A statistical diagram showing frequency density against distances in metres.

    The statistical diagram shown is a histogram.

  • True or False?

    The height of a bar in a histogram is equal to the frequency of that class.

    False.

    The height of a bar in a histogram is not equal to the frequency of that class.

    The height is equal to the frequency density.

  • True or False?

    The area of a bar in a histogram is proportional to its frequency.

    True.

    The area of a bar in a histogram is proportional to its frequency.

    In most cases the area is equal to the frequency.

  • How can you find the frequency of a group from a histogram?

    The frequency of a histogram is proportional to the area of the bar.

    Therefore, in order to find the frequency for a particular bar, you can find its area by multiplying the height (frequency density) by the width of the bar (class width).

    frequency equals frequency space density cross times class space width

  • How can you find the frequency of a part of a class interval from a histogram?

    To estimate the frequency of part of a class interval within a histogram:

    • Find the area of the bar for the part of the interval required.

Previous:Statistical DiagramsNext:Cumulative Frequency & Box Plots

    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