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Welcome to GCSE Edexcel Maths revision.

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Topic M 40: Tables, charts and averages.

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This video covers Foundation and Higher tiers.

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Frequency is how often a value or category occurs.

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A frequency table should identify values or categories, counts and the total sample size.

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Bar charts show categorical or discrete groups with equal-width separated bars; height represents frequency.

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Label axes and use a consistent scale.

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Separated bars for travel categories

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A pictogram uses symbols for counts.

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State the key and use fractional symbols consistently; if one symbol means 4, a half-symbol represents 2.

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A pie chart shows proportions of a total.

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Sector angle equals the fraction with numerator open bracket category frequency close bracket and denominator open bracket total frequency close bracket ,

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end fraction multiplied by 360 degrees.

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With 12 of 30 students, the sector is 144 degrees.

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A vertical-line chart represents ungrouped discrete numerical values.

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A time-series line graph connects measurements in time order; it is not the same as a scatter graph.

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Look for misleading displays: truncated axes, unequal spacing, inconsistent symbol areas and omitted categories can exaggerate a difference.

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Mean equals the fraction with numerator open bracket sum of values close bracket and denominator open bracket number of values close bracket , end fraction .

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Median is the middle value after ordering; for an even count, average the two middle values.

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Mode is the most frequent value; a set may have no unique mode.

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Range equals largest value minus smallest value.

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It describes spread, not the typical value, and is sensitive to extreme observations.

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Worked example: For 2, 3, 3, 4, 8, the mean is 4, median 3, mode 3 and range 6.

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The high value 8 raises the mean more than the median.

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Choose an average for the context.

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Median often describes a skewed set of incomes better than mean because a few very high incomes can pull the mean upwards.

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For a frequency table,

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mean equals the fraction with numerator open bracket the sum of fx close bracket and denominator open bracket the sum of f close bracket ,

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end fraction ,

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where x is a value and f is its frequency.

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Multiply each value by its frequency before adding. the sum of means sum of.

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Worked example: Values 1, 2, 3 have frequencies 2, 5, 3.

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Mean equals the fraction with numerator open bracket 1 multiplied by 2 plus 2 multiplied by 5 plus 3 multiplied by 3 close bracket and denominator open bracket 2 plus 5 plus 3 close bracket ,

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end fraction equals 21 over 10 equals 2.1.

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For continuous grouped data, use each class midpoint as its representative value.

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The resulting mean is an estimate because exact individual values are unknown.

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Worked example: Classes 0 is less than or equal to x is less than 10,

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10 is less than or equal to x is less than 20 and 20 is less than or equal to x is less than 30 have frequencies 2,

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5,

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3.

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Midpoints 5,

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15,

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25 give estimated mean the fraction with numerator open bracket 10 plus 75 plus 75 close bracket and denominator open bracket 10 close bracket ,

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end fraction equals 16.

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The modal class has the greatest frequency.

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Use cumulative totals to locate the class containing the median; grouped tables alone do not give an exact median value.

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When combining groups, add their totals and counts, not simply their means.

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Two people averaging 10 and eight people averaging 20 have combined mean the fraction with numerator open bracket 2 multiplied by 10 plus 8 multiplied by 20 close bracket and denominator open bracket 10 close bracket ,

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end fraction equals 18.

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Explain comparisons using both average and spread.

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Check sample sizes, outliers and whether the groups were measured consistently before drawing a conclusion.

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That completes Tables, charts and averages.

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Revisit the notes and test yourself on the revision website.