Statistics
Averages, range, charts, scatter graphs and sampling.
Learn
Statistics, explained point by point
Everything the GCSE specification expects you to be able to do, and how to actually do it - the same lesson a signed-in student studies from.
Draw and interpret bar charts, pictograms and pie charts
Bar charts compare categories with gaps between bars; pictograms need a key (half a symbol means half the value). Pie chart angles come from proportions: with 40 people, each is 360 ÷ 40 = 9°, so a group of 12 gets 108°. Angles must total 360°.
Calculate the mean, median, mode and range, and choose the best average to use
Mean: total ÷ count. Median: middle of the ORDERED list. Mode: most common. Range measures spread, not average. The mean uses all the data but one extreme value drags it - the median resists outliers, which is why house prices are quoted as medians.
Find averages from frequency tables, including estimating the mean of grouped data
Multiply each value by its frequency, total, and divide by the TOTAL FREQUENCY - not by the number of rows. Grouped data hides exact values, so use each group's midpoint: the answer is an estimate, and saying why (the raw values are unknown) is part of the answer.
Draw and interpret scatter graphs, describe correlation, and use a line of best fit
Each point is one individual measured twice. An uphill drift is positive correlation, downhill negative, no pattern none. A line of best fit follows the trend with points balanced either side; predictions read off it are estimates - and stretching beyond the data (extrapolating) is unreliable.
Compare two distributions using an average and the spread
A full comparison quotes one average AND one measure of spread, in context: "Class A's median was higher, so they typically scored better; A's range was smaller, so they were more consistent." One sentence per measure, always tied back to the situation.
Draw and interpret cumulative frequency graphs and box plotsHigher only
Cumulative frequency is a running total, plotted at each group's UPPER boundary and joined with a smooth curve. Reading across at the half and quarter marks gives the median and quartiles; the interquartile range is the middle half's spread. Box plots display the same five-figure summary.
Draw and interpret histograms with unequal class widthsHigher only
With unequal classes, the AREA of each bar represents frequency, so the vertical axis is frequency density = frequency ÷ class width. A frequency of 30 over a width of 10 plots at height 3. To read a histogram, reverse it: frequency = density × width.
Practice
Try a Statistics question
A GCSE-style original question from this topic. Have a go before you open the working - deciding on an answer first is what makes the working stick.
A frequency table shows the number of siblings of 20 students: 0 siblings (frequency 5), 1 sibling (frequency 8), 2 siblings (frequency 4), 3 siblings (frequency 3). Work out the mean number of siblings.
- 1.25
- 6.25
- 1.5
- 1.2
Show the answer and the working
Answer: 1.25
Multiply each value by its frequency, total those products (25), then divide by the total frequency (20): 25 ÷ 20 = 1.25.
- Multiply each value by its frequency: 0×5 = 0, 1×8 = 8, 2×4 = 8, 3×3 = 9.
- Add the products: 0 + 8 + 8 + 9 = 25.
- Total frequency: 5 + 8 + 4 + 3 = 20.
- Mean = 25 ÷ 20 = 1.25.