Statistical investigative questions
A statistical question is one whose answer comes from data that varies. "How tall am I?" has one answer. "How tall are the students in my class?" has many answers, so it is statistical.
An investigation has four steps:
- Ask a clear question (who, what, which group).
- Collect data (survey, measuring, counting).
- Organise and show it (tally, frequency table, bar graph).
- Analyse and answer (find mean, median or mode; say what the data tells you).
A good question names the group and something you can measure or count.
Mean, median and mode
Mean (average) = sum of all values ÷ number of values. It is the fair share if everything were split equally.
Median = the middle value after putting data in order. If there are n values and n is odd, it is the ((n + 1) ÷ 2)th value. If n is even, it is the average of the two middle values.
Mode = the value that appears most often. There can be one mode, more than one, or none.
From a frequency table (value x, frequency f): mean = Σfx ÷ Σf.
Which average should I use?
- Use the mean when the values are close to each other (marks of a class).
- Use the median when a few values are very big or very small (salaries, house prices). One very big value pulls the mean up but hardly moves the median.
- Use the mode for the most popular choice, even for non-number data (favourite colour, shoe size).
Weighted average
Sometimes some values are more important. Each value x gets a weight w (how many times it counts).
Weighted average = (w₁x₁ + w₂x₂ + …) ÷ (w₁ + w₂ + …)
Example: 2 kg of rice at ₹40 and 3 kg at ₹50. Average price = (2 × 40 + 3 × 50) ÷ 5 = ₹46 per kg, not ₹45, because there is more of the costly rice. Weights can also be percentages that add up to 100%.
Stacked and 100% stacked bar graphs
A stacked bar graph draws one bar per group, and splits each bar into coloured parts placed on top of each other. The full height shows the total; each colour shows a part.
A 100% stacked bar graph makes every bar the same height (100%). Each part shows its percentage: part ÷ total × 100. Use it when totals are different but you want to compare shares fairly.
Always add a legend (which colour means what) and a title.
Board exam pattern
Statistics and Probability carries 10 marks in CBSE Class 9 (2026-27). Expect: find mean, median and mode of raw data or a frequency table, a weighted average (marks or prices), reading and drawing a stacked or 100% stacked bar graph, and choosing a good statistical question.
Try it at home
Ask 10 family members or friends: "How many hours did you sleep last night?" Write the numbers. Find the mean, the median and the mode. Which one describes your group best? Then ask your friends in two classes how they come to school and draw a 100% stacked bar for each class.
Key formulas and definitions
- Mean = sum of values ÷ number of values
- Mean from a frequency table = Σfx ÷ Σf
- Median (n odd) = ((n + 1) ÷ 2)th value in order
- Median (n even) = average of the (n ÷ 2)th and (n ÷ 2 + 1)th values
- Mode = value with the highest frequency
- Weighted average = Σwx ÷ Σw
- Percentage in a 100% stacked bar = part ÷ total × 100
Worked examples
1. Which is a statistical investigative question: (a) How many pencils are in my bag? (b) How many pencils do students in Class 9 carry?
(b). Its answer varies from student to student, so we must collect data. (a) has just one answer.
2. Find the mean of 12, 15, 18, 20 and 25.
Sum = 90. Number of values = 5. Mean = 90 ÷ 5 = 18.
3. Find the median of 3, 8, 5, 10, 7, 12.
In order: 3, 5, 7, 8, 10, 12. There are 6 values (even), so median = (7 + 8) ÷ 2 = 7.5.
4. Shoe sizes of 20 children: size 5 (3 children), 6 (8), 7 (6), 8 (3). Find the mode, median and mean.
Mode = 6 (highest frequency 8). Median: 10th and 11th values are both 6, so median = 6. Mean = (5×3 + 6×8 + 7×6 + 8×3) ÷ 20 = 129 ÷ 20 = 6.45.
5. A shop mixes 2 kg of rice at ₹40/kg with 3 kg at ₹50/kg. What is the average price per kg?
Weighted average = (2 × 40 + 3 × 50) ÷ (2 + 3) = 230 ÷ 5 = ₹46 per kg.
6. Projects count 20%, tests 30% and the final exam 50%. Riya scores 90, 70 and 80. Find her final score.
0.2 × 90 + 0.3 × 70 + 0.5 × 80 = 18 + 21 + 40 = 79.
7. Class A has 30 students: 12 like cricket, 18 like football. Class B has 50: 25 like cricket, 25 football. Draw the 100% stacked bar values.
Class A: cricket 12 ÷ 30 × 100 = 40%, football 60%. Class B: cricket 50%, football 50%. Both bars are 100% tall; B's cricket part is taller even though A has fewer students.
8. The mean of 5 numbers is 12. Four of them are 6, 14, 9 and 11. Find the fifth.
Total = 5 × 12 = 60. Four numbers add to 40. Fifth = 60 − 40 = 20.
Common mistakes
- Finding the median without first putting the data in order.
- For an even number of values, picking one middle value instead of averaging the two middle values.
- In a weighted average, dividing by the number of values instead of by the sum of the weights.
- Comparing raw heights of stacked bars when group totals are different; use a 100% stacked bar to compare shares.