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Mean, Median and Mode — REET Maths Notes

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This page covers REET maths' 'Mean, Median and Mode' topic as per the syllabus — definitions, formulas, and worked examples with self-checked calculations are explained in simple language. This topic is included in the statistics section for both REET Level 1 and Level 2 maths papers, so knowing exactly how the three measures differ and how to calculate each one matters.

  • 0 questions in REET 2024 (syllabus-based notes)
  • Class 7–8 level
  • 8 min read
Verified 17 September 2026 · Source: BSER — REET आधिकारिक सिलेबस व 2024 प्रश्न-पत्र (मूल PDF; बोर्ड पोर्टल पर अब उपलब्ध नहीं)

How this topic is asked in REET

No direct question on 'Mean, Median and Mode' was found in the REET 2024 paper records, yet it's included in the statistics section (Class 7-8 level) of the official BSER maths syllabus, and questions that ask you to find a measure of central tendency from a small data set are common in competitive exams generally. The notes below are based on the syllabus wording and self-checked calculations — no imagined 'previous question' has been used.

Basic definitions

The mean is the average of all the observations in a data set: mean = (sum of all values) ÷ (number of values). It's the most commonly used measure of central tendency, but a single unusually large or small value (an outlier) can make it misleading.

The median is the value that sits exactly in the middle once the data is arranged in ascending order. If the number of values (n) is odd, the median is the (n+1)/2-th term; if n is even, the median is the average of the n/2-th and (n/2+1)-th terms. The mode is the value that occurs most often in the data — a data set can have more than one mode, or no mode at all.

Formulas worth knowing

Mean
sum of all values ÷ number of values
Median (n odd)
the (n+1)/2-th term (in ascending order)
Median (n even)
average of the n/2-th and (n/2+1)-th terms
Mode
the value that occurs most often
Measure most affected by outliers
mean — it's affected the most by a single unusually large or small value

Worked examples

DataMean, median, mode
10, 20, 30, 40, 50mean = 150/5 = 30; median (n=5, odd) = the middle term = 30; mode = none (all values are different)
2, 3, 3, 5, 7, 3, 8 (ascending order: 2,3,3,3,5,7,8)mean = 31/7 ≈ 4.43; median (n=7) = the 4th term = 3; mode = 3 (appears three times)
5, 8, 12, 15, 20, 25 (n=6, even)mean = 85/6 ≈ 14.17; median = (12+15)/2 = 13.5

Every value here has been added up and ordered and self-checked.

Mean, median and mode from a frequency table

When data is given in a frequency table, find the mean by multiplying each value by its frequency, adding these up, and then dividing by the total frequency. Example: the marks of 11 students are as follows — mark 5 (2 students), mark 6 (5 students), mark 7 (3 students), mark 8 (1 student). Total students = 2+5+3+1 = 11.

Mean = (5×2 + 6×5 + 7×3 + 8×1) ÷ 11 = (10+30+21+8) ÷ 11 = 69/11 ≈ 6.27. Mode = 6 (the highest frequency, 5 students). For the median, look at the 6th term — cumulative frequency: up to mark 5 it's 2, up to mark 6 it's 2+5=7; so the 6th term falls in the mark-6 group, meaning the median = 6.

Another worked example

The exam marks of 10 students are as follows: 45, 50, 55, 60, 65, 70, 75, 80, 85, 90. Find their mean and median. Solution: sum = 45+50+55+60+65+70+75+80+85+90 = 675. Mean = 675/10 = 67.5. n=10 (even), median = average of the 5th and 6th terms (65 and 70) = (65+70)/2 = 67.5.

In this example, the mean and median both came out equal (67.5) — this happened because the data is spaced at equal intervals (a gap of 5 each time), meaning it forms an arithmetic progression. When data is spread out this symmetrically, the mean and median come out equal or very close — this helps students understand the shape of a data set.

On the other hand, if one extreme value is added to this same set — say an 11th student whose score is recorded (by mistake, or for some unusual reason) as 300 — then the new mean = (675+300)/11 = 975/11 ≈ 88.6, which will look far higher than the real performance of everyone else. The median, meanwhile, stays almost unaffected by this single extreme value — which is exactly why the median is considered a more reliable measure for real-world data with unusual values (such as income).

How to teach this to children

Activity

Measure the height (or shoe size) of every student in the class to collect real data, then have them find the mean, median and mode themselves from it — this connects the idea of statistics directly to everyday life.

Teaching aid

Arranging the data in ascending order along a strip or line (like a human chain) and showing the median as 'the student standing in the middle' works well to explain the concept.

Common misconception

Students often try to find the median without ordering the data first, or think the mean and mode are the same value — always remind them to arrange data in ascending order first, every single time.

Assessment idea

Give students a data set that includes one very large value (an outlier), and ask which measure — mean or median — was less affected by it, to check their understanding of the difference between the two.

A trick worth remembering

Always arrange the data in ascending order before finding the median — this is the most common place mistakes happen. When n is odd, the median is directly the middle term; when n is even, take the average of the two middle terms — remember it as 'shared when even, direct when odd'.

Practice questions

Question 1

Find the mean of the data 12, 15, 18, 21, 24.

  1. A20
  2. B17
  3. C21
  4. D18

Explanation

Sum = 12+15+18+21+24 = 90. Mean = 90/5 = 18.

Question 2

Find the median of the data 23, 29, 20, 25, 18.

  1. A20
  2. B24
  3. C23
  4. D25

Explanation

In ascending order: 18, 20, 23, 25, 29. n=5 (odd), median = (5+1)/2 = the 3rd term = 23.

Question 3

Find the mode of the data 4, 5, 6, 4, 7, 4, 8, 5.

  1. A8
  2. B4
  3. C5
  4. D6

Explanation

The value 4 occurs three times, more often than any other value (5 occurs twice, the rest once each); so the mode = 4.

Question 4

Find the median of the data 10, 15, 20, 25, 30, 35.

  1. A22.5
  2. B20
  3. C25
  4. D21

Explanation

n=6 (even). Median = average of the 3rd and 4th terms = (20+25)/2 = 22.5.

Question 5

The mean of 5 numbers is 20. If one number is removed, the mean of the remaining 4 becomes 19. Find the removed number.

  1. A20
  2. B19
  3. C24
  4. D16

Explanation

Sum of 5 numbers = 20×5 = 100. Sum of the remaining 4 = 19×4 = 76. Number removed = 100−76 = 24.

Question 6

If the mean of n observations x₁, x₂, ..., xₙ is M, and 5 is added to each observation, what is the new mean?

  1. A5M
  2. BM + 5
  3. CM/5
  4. DM

Explanation

When the same number (5) is added to every observation, the mean increases by that same number, because the total increases by n×5 while you still divide by n — so the new mean is M+5.

Question 7

Find the mode of the data 3, 3, 3, 5, 5, 7, 9, 9, 9, 9.

  1. A7
  2. B3
  3. C5
  4. D9

Explanation

The value 9 occurs four times (3 occurs three times, 5 occurs twice, 7 occurs once), which is the highest frequency; so the mode = 9.

Question 8

Find the mean of the first five natural numbers (1, 2, 3, 4, 5).

  1. A3
  2. B4
  3. C2.5
  4. D15

Explanation

Sum = 1+2+3+4+5 = 15. Mean = 15/5 = 3.

Question 9

Which is the most suitable real-life example to teach mean, median and mode in Class 8?

  1. Aकेवल सूत्र रटवाना, बिना किसी उदाहरण के
  2. Bकक्षा के सभी विद्यार्थियों की ऊँचाई मापकर स्वयं उसका माध्य, माध्यिका व बहुलक निकलवाना
  3. Cइस टॉपिक के लिए किसी गतिविधि की आवश्यकता नहीं
  4. Dआँकड़े दिए बिना केवल परिभाषा याद करवाना

Explanation

Collecting real data and calculating it themselves helps students understand the usefulness of statistics and connects the concept to everyday life, which teaches far more durably than rote learning.

Question 10

An outlier in a data set has the greatest effect on which measure of central tendency?

  1. Aबहुलक (mode)
  2. Bमाध्यिका (median)
  3. Cमाध्य (mean)
  4. Dइनमें से कोई नहीं

Explanation

The mean depends on the sum of all values, so a single unusually large or small value (an outlier) changes it quickly, while the median and mode stay relatively stable.

Frequently asked questions

How many questions come from 'Mean, Median, Mode' in the REET exam?+

No direct question from this topic was found on record in REET 2024, but it is included in the statistics section of the official BSER maths syllabus, so preparing it is necessary.

Which of mean, median and mode is affected the most by an outlier?+

The mean is affected the most by an unusually large or small value, while the median and mode are affected much less.

How do you find the median for an even number of values?+

After arranging the data in ascending order, the median is found by averaging the two middle terms (the n/2-th and n/2+1-th).

Can a data set have more than one mode?+

Yes, if two or more values occur with the same highest frequency, the data set can have more than one mode (bimodal/multimodal), and if all values are different, there is no mode at all.

When do the mean and median come out equal?+

When the data is spaced at equal, symmetric intervals (like an arithmetic progression), the mean and median usually come out equal or very close; a single outlier can break this equality.

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REET Syllabus 2024

See the complete official REET Level 1 and Level 2 syllabus, subject-wise.

REET 2024 Solved Papers

Read the REET 2024 previous papers with answers and explanations.

Official Sources

  1. BSER — REET आधिकारिक सिलेबस व 2024 प्रश्न-पत्र (मूल PDF; बोर्ड पोर्टल पर अब उपलब्ध नहीं)

Change Log

  • 17 September 2026 — English page published — mirrors the fact-checked Hindi page, independently bilingual-accuracy checked