Statistics

Statistics starts with a question and data, then uses suitable graphs and measures to support a fair conclusion. The current course includes weighted averages and stacked bar graphs.

Core ideas

Start with a specific investigative question, define what is being measured, collect an appropriate sample, organise and visualise the data, then interpret the result with its limitations.

Mean=sum of values÷number of values; median=middle value after sorting (or the average of the two middle values); mode=most frequent value. For groups with different sizes, a weighted mean is Σ(weight×value)÷Σ(weight).

A stacked bar shows parts that add to each whole; a 100% stacked bar converts each whole to 100%, making proportions easier to compare. Read the legend and axis carefully before comparing groups.

Worked examples

Weighted average

Group A has 20 students with mean score 70; Group B has 30 students with mean 80. Combined mean=(20×70+30×80)/(20+30)=3,800/50=76.

Read a 100% stacked bar

If 40% of Group A and 55% of Group B chose option X, the share choosing X is 15 percentage points higher in Group B. This comparison does not tell us the groups’ absolute counts unless group sizes are known.

Mean, median and mode

For 4, 6, 6, 8, 11, mean=7, median=6 and mode=6. The median may be more representative if one value is unusually large.

Practice questions with answers

Find the weighted mean of 10 items scored 6 each and 20 items scored 9 each.

(10×6+20×9)/(10+20)=240/30=8.

Why use a 100% stacked bar graph?

It compares the proportion each category contributes to the whole across groups of different totals.

Find the median of 3, 9, 4, 7.

Order the data: 3, 4, 7, 9. Median=(4+7)/2=5.5.

Practical investigation

Ask a clear, non-sensitive question such as “How did classmates travel to school today?” Record a small class sample, make a frequency table and a suitable graph. If group sizes differ, compare percentages using a 100% stacked bar; note that the sample is not necessarily representative of all students.

Was the question neutral and clear?
Does the graph match the data type?
Does the conclusion stay within what the sample supports?

These are original revision notes aligned to the CBSE Class IX 2026–27 curriculum. Use them with your prescribed NCERT book and your teacher’s directions. Official CBSE syllabus · Official NCERT textbook resource