Histograms

OCR

GCSE

Histograms represent grouped continuous data where the area of each bar is proportional to the frequency, distinguishing them from bar charts where height represents frequency. This graphical method necessitates the calculation of frequency density to accurately plot distributions with unequal class widths. Candidates must rigorously apply class boundaries to ensure continuity between intervals, avoiding gaps inherent in discrete data notation. Mastery involves both the construction of accurate diagrams and the inverse process of interpreting areas to reconstruct frequency tables or estimate statistical measures such as the median via linear interpolation.

Objectives

Exam Tips

Pitfalls

Key Terms

Mark Points

What You Need to Demonstrate

Key skills and knowledge for this topic

Award M1 for the correct calculation of frequency density (Frequency ÷ Class Width) for at least two intervals
Award A1 for drawing bars with correct widths and heights based on calculated frequency densities
Award B1 for correctly labelling the vertical axis as 'Frequency Density' (abbreviations like FD are usually accepted)
Award M1 for using the principle 'Frequency = Area' to calculate missing frequencies or total population size
Award M1 for using midpoints of class intervals combined with calculated frequencies to estimate the mean

Example Examiner Feedback

Real feedback patterns examiners use when marking

"You have plotted the frequency directly — remember that for unequal class widths, the height must be the Frequency Density"
"Check your class widths again; look closely at the inequalities to determine the exact interval size"
"Good graph construction, but you missed the axis label. Examiners require 'Frequency Density' to be stated"
"To access the top marks, show your working for the 'Area = Frequency' calculation explicitly"

Marking Points

Key points examiners look for in your answers

Award M1 for the correct calculation of frequency density (Frequency ÷ Class Width) for at least two intervals
Award A1 for drawing bars with correct widths and heights based on calculated frequency densities
Award B1 for correctly labelling the vertical axis as 'Frequency Density' (abbreviations like FD are usually accepted)
Award M1 for using the principle 'Frequency = Area' to calculate missing frequencies or total population size
Award M1 for using midpoints of class intervals combined with calculated frequencies to estimate the mean

Examiner Tips

Expert advice for maximising your marks

💡Always write down the column for Frequency Density (FD) next to the table before starting to draw; this secures method marks even if the graph is inaccurate
💡When solving 'missing scale' problems, identify one complete bar where both width and frequency are known to establish the 'Area = k × Frequency' relationship
💡For questions asking to 'Estimate the mean', remember to calculate the midpoint of each class interval first, then multiply by the frequency (Area), not the height

Common Mistakes

Pitfalls to avoid in your exam answers

Plotting frequency directly on the vertical axis instead of calculating frequency density
Incorrectly determining class widths from inequality notation (e.g., treating '10 < x ≤ 15' as a width of 4 or 6 instead of 5)
Failing to label the vertical axis, or labelling it incorrectly as 'Frequency'
Calculating the mean using frequency density values instead of the actual frequencies derived from the bar areas

Key Terminology

Essential terms to know

Frequency Density calculation and application

Area proportionality (Frequency = Area)

Determination of Class Boundaries and Widths

Linear Interpolation for Median and Quartiles

Interpretation of Skewness and Distribution Shapes

Likely Command Words

How questions on this topic are typically asked

Construct

Calculate

Estimate

Complete

Show that

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