Class 11 Maths · Original EZT practice
Statistics (Class 11 Chapter 13): summary and practice
Statistics here means measuring spread: the range, mean deviation about the mean or median, and variance with its square root, the standard deviation - for raw data and for frequency distributions, including the shortcut and step-deviation methods. All questions are original EZT tutor practice following the chapter's own section order.
6 original worked examples, 6 fresh self-check questions and 4 mixed questions, with explained answers. These are not copied textbook exercises, an official chapter index or a full answer key. No affiliation with NCERT is claimed.
Official sources for topic and edition context, checked 22 October 2026:
1. Dispersion and range
Central tendency says where data sits; dispersion says how spread out it is. The range is the simplest measure: maximum minus minimum.
2. Mean deviation
The mean of the absolute deviations from a central value - the mean or the median. Computed for ungrouped data and for grouped (discrete and continuous) data; its limitation is that ignoring signs makes it algebraically awkward.
3. Variance and standard deviation
Variance is the mean of the SQUARED deviations from the mean; standard deviation is its square root, returning to the original units. Sections 13.5.2 and 13.5.3 extend both to frequency distributions.
4. Shortcut and step-deviation methods
With an assumed mean a (and class width h), coded values turn heavy sums into light ones: variance of the coded data rescales to variance of the original, and the mean shifts back by adding a.
Choose, solve, check, then try a fresh question.
Before calculating, read the method prompt and name the condition that makes it useful. Write your own attempt. Open the steps only when you need them, and use the check to catch a wrong sign, unit or interpretation. Finish with the fresh question before reading its answer.
Variance and standard deviation of raw data
Choose the method: Variance = sum of squared deviations from the mean, divided by n; SD = square root of variance.
EZT practice question
Find the variance and standard deviation of 4, 6, 8, 10, 12.
Show the worked solution
- Mean = (4 + 6 + 8 + 10 + 12)/5 = 8.
- Deviations: -4, -2, 0, 2, 4; squared: 16 + 4 + 0 + 4 + 16 = 40.
- Variance = 40/5 = 8; SD = sqrt(8) = 2.83 (about).
Answer: Variance 8, standard deviation about 2.83.
Check: Every squared deviation is non-negative, so variance can never be negative - and SD must lie between the smallest and largest absolute deviation, here 0 and 4. 2.83 fits.
Watch for this: Do not forget the final square root - variance 8 is not the standard deviation.
Now try it yourself
Variance of 2, 4, 6, 8, 10?
Check your answer
8.
Same spread around mean 6.
Range of a data set
Choose the method: Range = maximum - minimum.
EZT practice question
Find the range of 4, 6, 8, 10, 12.
Show the worked solution
- Maximum = 12.
- Minimum = 4.
- Range = 12 - 4 = 8.
Answer: 8.
Check: The range uses only the two extremes - it cannot exceed the gap between them, and it ignores everything in between, which is exactly its weakness.
Watch for this: The range is a single number, not the interval from 4 to 12.
Now try it yourself
Range of 15, 3, 27, 9?
Check your answer
24.
27 - 3.
Mean deviation about the mean
Choose the method: Take absolute deviations from the mean, then average them.
EZT practice question
Find the mean deviation about the mean for 4, 6, 8, 10, 12.
Show the worked solution
- Mean = 8.
- Absolute deviations: 4, 2, 0, 2, 4 - sum 12.
- Mean deviation = 12/5 = 2.4.
Answer: 2.4.
Check: Mean deviation must be smaller than the largest absolute deviation (4) and, being an average of positives, at least 0 - 2.4 sits sensibly between.
Watch for this: Do not average the SIGNED deviations - those always sum to zero about the mean, which tells you nothing.
Now try it yourself
Mean deviation about the mean for 2, 4, 6, 8, 10?
Check your answer
2.4.
Same absolute deviations about mean 6.
Mean deviation about the median
Choose the method: Same idea, anchored at the median instead of the mean.
EZT practice question
Find the mean deviation about the median for 3, 5, 9, 11, 17.
Show the worked solution
- Median (middle value) = 9.
- Absolute deviations from 9: 6, 4, 0, 2, 8 - sum 20.
- Mean deviation = 20/5 = 4.
Answer: 4.
Check: The median MINIMISES the sum of absolute deviations, so deviation about the median can never exceed deviation about the mean - a quick sanity relation.
Watch for this: Read the question twice: deviation about the MEAN and about the MEDIAN are different computations with different answers.
Now try it yourself
Median of 3, 5, 9, 11, 17 and the deviation of the largest value from it?
Check your answer
Median 9, deviation 8.
17 - 9.
Step-deviation shortcut
Choose the method: Code values as u = (x - a)/h; find variance of u, then multiply by h^2.
EZT practice question
For 4, 6, 8, 10, 12 with assumed mean a = 8 and h = 2, find the variance by step deviation.
Show the worked solution
- Coded values u: -2, -1, 0, 1, 2.
- Mean of u = 0; variance of u = (4 + 1 + 0 + 1 + 4)/5 = 10/5 = 2.
- Variance of x = h^2 x variance of u = 4 x 2 = 8.
Answer: 8 - matching the direct method.
Check: The shortcut must reproduce the direct answer exactly; 8 = 8, so the coding is consistent.
Watch for this: The variance rescales by h^2, not by h - forgetting the square halves or doubles the answer.
Now try it yourself
With a = 6, h = 2, coded values for 2, 4, 6, 8, 10?
Check your answer
-2, -1, 0, 1, 2.
(x - 6)/2.
Why the square root matters
Choose the method: Variance carries squared units; standard deviation returns to the original unit.
EZT practice question
Heights measured in cm have variance 25 cm^2. What is the standard deviation, and why quote it?
Show the worked solution
- SD = sqrt(25) = 5.
- The variance's unit is cm^2 - an area, not a height.
- SD 5 cm is directly comparable with the data.
Answer: 5 cm.
Check: 5 cm is a believable spread for heights; 25 cm^2 cannot even be drawn on the same axis as the data.
Watch for this: Quoting spread in squared units hides its size - always finish with the square root.
Now try it yourself
Variance 100 (marks^2) - standard deviation?
Check your answer
10 marks.
sqrt(100) = 10.
Try a mixed set
Choose a method or explanation before opening each answer.
1. Range?
Show answer and reason
Maximum - minimum.
The quickest spread measure, and the crudest.
2. Variance formula (raw data)?
Show answer and reason
Sum of (xi - mean)^2, divided by n.
Mean of squared deviations.
3. Standard deviation?
Show answer and reason
Square root of variance.
Back to the original units.
4. In step deviation, variance rescales by?
Show answer and reason
h^2.
Coding divided by h, so variance divides by h^2.
Try it yourself
Work these on paper before checking any notes. Answers are deliberately not shown here.
- Variance of 2, 4, 6, 8, 10.
- Mean deviation about the mean for 2, 4, 6, 8, 10.
- Standard deviation when the variance is 100.
Know the rule but lose track of the steps?
Bring your book edition, your school topic list and a question you attempted. Ask a tutor to explain the choice of method and test it with a different problem. Agree the lesson topics, schedule and fee before starting.
For cost context, see home tuition fees in Delhi NCR. Agree the topics, schedule and fee with your chosen tutor.
Questions about this practice page
- What does dispersion measure?
- How spread out the data is around its centre. Two data sets can share a mean of 8 and behave completely differently - one clustered tight, one scattered. Range, mean deviation, variance and standard deviation each capture that spread with increasing sophistication.
- Mean deviation or standard deviation - which should I use?
- The chapter presents both. Mean deviation is intuitive (average distance from the centre) but awkward algebraically because of the absolute values. Variance and standard deviation square the deviations instead, which makes them the standard tools for further work.
- When does the step-deviation method save work?
- When values are large or evenly spaced - typical of grouped data. Coding u = (x - a)/h turns numbers like 45, 55, 65 into -1, 0, 1; the variance of u is tiny to compute, and multiplying by h^2 rescales it.
- Why divide by n and not n - 1?
- This chapter works with the whole data set as given, so the divisor is n. The n - 1 divisor belongs to sample-based estimation, which is outside this chapter's scope - follow the book's convention here.
- Are these the NCERT exercise questions for Statistics (Class 11)?
- No. EZT pages are original practice following the chapter's section order - use them to prepare for the textbook exercises, not as a substitute for your book.