The water 100 flats on an estate used in a month is drawn as a cumulative frequency polygon, and from it 50% of the flats used less than 39.5 m³. How many flats used less than 39.5 m³?

50 flats. From a percentage to a number: the total × the percentage = 100 × 50% = 50.

Data and probability · Ages 14–15

Cumulative frequency & charts

From “Frequency polygons” to “Misleading statistical charts”, step by step, each skill with its methods, worked examples and answers.

Frequency polygonsPoints at the class marks; a 0 class at each end
Method40–49: class mark (40 + 49) ÷ 2 = 44.5
Another way: Join the bars' topsDraw the histogram, then join the middles of the bars' tops
Cumulative frequencyAdd as you go; to go back, subtract neighbours
MethodFrequencies 3, 5, 8, 4 → cumulative 3, 8, 16, 20
Another way: Subtract to go back16 − 8 = 8
Cumulative frequency polygonsPoints at upper boundaries; for 'at least', take from the total
Method40 in all, 30 below 59.5: 40 − 30 = 10 are at least 59.5
Another way: Make it a tableBoundaries 49.5, 59.5, 69.5 → cumulative 12, 30, 40
Interpreting frequency polygons and curvesCompare positions; percentage = number ÷ total × 100%
Method35 of 50 below 59.5: 35 ÷ 50 × 100% = 70%
Another way: From a percentage to a number50 × 70% = 35
Choosing a statistical chartCompare: bars. Parts of a whole: pie. Over time: line
MethodThe temperature over twelve months: a line graph
Another way: Rule charts outNot parts of a whole → no pie chart
Misleading statistical chartsFirst check whether the vertical axis starts at 0
MethodAxis from 50: 52 and 56 give bars 2 and 6 high
Another way: Compare the ratiosLooks 6 ÷ 2 = 3 times; really 56 ÷ 52 ≈ 1.08 times

From different skills in this topic. Have a go first, then open each one for the answer and the working.

Example 1Frequency polygons →
The frequency polygon shows the ages (in years) of a gym's members. How many are in the class with class mark 34.5?
Show the answer and working
Answer: 5 people
Go up from 34.5 on the axis: the point's height is the frequency, 5.
Example 2Interpreting frequency polygons and curves →
The water 100 flats on an estate used in a month is drawn as a cumulative frequency polygon, and from it 50% of the flats used less than 39.5 m³. How many flats used less than 39.5 m³?
Show the answer and working
Answer: 50 flats
From a percentage to a number: the total × the percentage = 100 × 50% = 50.
Example 3Misleading statistical charts →
The bar chart shows how many tubs of ice cream two branches sold in a week, its vertical axis starting at 80. Branch A sold tubs and branch B .
Fill in each blank
Show the answer and working
Answer: 82, 98
The axis starts at 80, so read each bar against the scale: A is 82, B is 98.

Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.

Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
Practice paper: Set out in parts like a school paper, marked, with answers and full working