Class 10 / Maths
Class 10 Maths Statistics Notes
Notes on mean, median, mode, grouped data, cumulative frequency, and ogives.
Topic introduction
Statistics helps students summarise data using mean, median, mode, and cumulative frequency. Class 10 questions often use grouped data, so setting up the table correctly is just as important as applying the formula.
Key points
- Mean, median, and mode are measures of central tendency.
- For grouped data, direct, assumed mean, and step-deviation methods can be used for mean.
- Median class is found using cumulative frequency and N/2.
- Mode uses the modal class, which has the highest frequency.
Definitions
Mean: The average value of a data set.
Median: The middle value when data is arranged in order, or the value that divides grouped data into two equal parts.
Mode: The value or class with the highest frequency.
Class mark: The midpoint of a class interval.
Ogive: A cumulative frequency curve.
Formulas
- Class mark = (lower limit + upper limit)/2
- Mean = sum of observations / number of observations
- Grouped mean = sum(fx) / sum(f)
- Median formula: l + [(N/2 - cf)/f] x h
- Mode formula: l + [(f1 - f0)/(2f1 - f0 - f2)] x h
Examples
- The class mark of 30-40 is (30 + 40)/2 = 35.
- For values 5, 7, 9, 11, 13, the mean is 45/5 = 9.
- If N = 80, use N/2 = 40 to locate the median class.
Mean of grouped data
Use direct method when calculations are simple. Use assumed mean or step-deviation when class marks are large.
Class mark is found by averaging the lower and upper limits of a class interval.
Median, mode, and ogive
The median divides data into two equal parts. Use cumulative frequency to locate the median class.
An ogive is a cumulative frequency graph and can be used to estimate median graphically.
Common mistakes
- Using class interval limits instead of class marks while calculating grouped mean.
- Choosing the median class from frequency instead of cumulative frequency.
- Calling the highest value the mode instead of the value or class with highest frequency.
- Forgetting to arrange raw data before finding median.
- Using N instead of N/2 to locate the median class.
Quick practice
- Find the class mark of 20-30.
- Find the mean of 2, 4, 6, 8, 10.
- What is the modal class?
- Explain how N/2 is used to locate the median class.
Related practice
For schools
Run your school with VyasNex School Management System
Use VyasNex for attendance, fees, report cards, parent communication, records, and daily school administration.