Chapter 12 · NCERT Class 9 Mathematics

Statistics

Statistics is the science of collecting, organising and making sense of data. Learn to turn a jumble of numbers into a frequency table, find its centre with the mean, median and mode, and picture it with bar graphs, histograms and frequency polygons. Tap each term to see exactly what it means.

📊 3 topics⏱ ~25 min📝 12-question quiz

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The language of statistics

Statistics has its own vocabulary for data and its centre. Tap each term to see what it means in one clear line.

Explore · Describing datatap a term

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The three big ideas

Data — facts or figures collected for a purpose. Primary data you collect yourself; secondary data comes from another source.
Raw (ungrouped) data is just as collected, unorganised. Grouped data is arranged into class intervals such as 0–10, 10–20, 20–30.
A frequency distribution table lists each value or class beside its frequency — how many times it occurs.

Mean (average) = sum of all observations ÷ number of observations.
Median = the middle value once the data is arranged in order; for an even count, average the two middle values.
Mode = the value that occurs most often.

Worked example. Find the mean of 4, 6, 8, 10, 12.

Mean = (4 + 6 + 8 + 10 + 12) ÷ 5 = 40 ÷ 5 = 8.

Common mistake: to find the median you must first arrange the data in order. Reading the middle of an unsorted list gives the wrong answer — and for an even number of values, remember to take the average of the two middle ones.

Bar graph: equal-width bars with gaps between them; used for discrete data or separate categories. Each bar's height shows its frequency.
Histogram: bars that touch (no gaps); used for grouped/continuous data with class intervals.
Frequency polygon: join the mid-points of the tops of the bars (the class mid-points) with straight line segments.

Where you'll meet it

Statistics, all around you

Cricket & sports averages

A batter's batting average is just the mean runs per innings; run rates, strike rates and bowling averages are all means worked out from match data — statistics scoring every game.

Surveys & the census

Governments and companies summarise huge surveys and the national census using the mean, median, mode and graphs — to report things like average household size or the most common age group.