Mean and Median Class 9 ICSE — Chapter 19
The mean and median class 9 icse chapter introduces the two core measures of central tendency. In this ICSE Class 9 Mathematics chapter, you learn the mean formula for ungrouped data, the five properties that govern the mean, and the three-step method for finding the median. Each section defines a term, states the rule, and shows a worked pattern you can copy for your own data.
Download Mean and Median Class 9 ICSE Mathematics Chapter 19 PDF
Download the Mean and Median Class 9 ICSE Mathematics chapter PDF to revise offline or print for practice. It is the full chapter as printed in the book — 8 pages, 3 sections, 24 questions.
What is inside Chapter 19
8 pages · 3 sections · 11 worked examples · 24 exercise questions
| Section | Title |
|---|---|
| 19.1 | MEAN OF UNGROUPED DATA |
| 19.2 | PROPERTIES OF MEAN |
| 19.3 | MEDIAN |
- EXERCISE 19(A): 14 questions
- EXERCISE 19(C): 10 questions
19.1 MEAN OF UNGROUPED DATA
The mean is the most common measure of central tendency. In this ICSE chapter, the words mean, arithmetic mean, and average all mean the same thing. For n observations x_1, x_2, \ldots, x_n, the mean \bar{x} is their sum divided by n.
\bar{x} = \frac{x_1 + x_2 + \cdots + x_n}{n} = \frac{1}{n}\sum_{i=1}^{n} x_i
The symbol \Sigma (capital Greek sigma) means “sum of”. The shorthand \Sigma x stands for x_1 + x_2 + \cdots + x_n, the total of all observations. The rule is simple: divide the sum by the total number of observations n.
Worked pattern. Find the mean of 15, 18, 21, 24 and 27. First add them: 15 + 18 + 21 + 24 + 27 = 105. Here n = 5. So the mean is \bar{x} = 105/5 = 21. One number now represents the whole set.
Fraction result. The mean need not be a whole number. Take the first five odd primes 3, 5, 7, 11 and 13. Their sum is 39 and n = 5. So \bar{x} = 39/5 = 7.8. The same pattern appears whenever the sum does not divide evenly.
Common mistake. Dividing by the wrong n is the most frequent error. Count the observations you actually summed. Also remember that \Sigma x is the total, not the mean — you must still divide by n.
19.2 PROPERTIES OF MEAN
The mean follows five rules that let you predict how it changes without re-summing the data. Property 1 states that the sum of deviations from the mean is always zero: \Sigma(x - \bar{x}) = 0. Each deviation is the difference between one observation and the mean. The positive and negative differences always cancel out.
Properties 2 to 5 describe what happens when you change every observation by the same amount a.
| Property | Change to each observation | New mean |
|---|---|---|
| 2 | Add a | \bar{x} + a |
| 3 | Subtract a | \bar{x} - a |
| 4 | Multiply by a | a\bar{x} |
| 5 | Divide by a | \bar{x}/a |
Worked pattern. Take the data 10, 20, 30, 40. The mean is 100/4 = 25. Add 5 to every value, the new mean is 25 + 5 = 30. Subtract 5, it becomes 20. Multiply by 3, it becomes 75. Divide by 2, it becomes 12.5. You never re-sum the whole set.
Correction pattern. A common board-style question gives a wrong mean and asks for the correct one. Suppose the mean of 50 observations is 100, and one value 95 was misread as 59. The incorrect total is 50 \times 100 = 5000. The correct total is 5000 - 59 + 95 = 5036. The correct mean is 5036/50 = 100.72. The common error is adjusting the mean directly — always fix the total \Sigma x first.
Unknown observation. To find a missing value p, write the mean formula with p included. If the mean of 6, 9, 12, p and 18 is 12, then (45 + p)/5 = 12. So 45 + p = 60 and p = 15.
19.3 MEDIAN
The median is the value of the middle term in an ordered data set. It splits the data into two equal halves. The median does not use every value — only the position of the middle matters.
The three steps. Finding the median always follows the same order.
- Step 1: Arrange the data in ascending or descending order of magnitude.
- Step 2: Count the total number of observations n.
- Step 3: Apply the odd or even rule below.
If n is odd, the median is the \left(\frac{n+1}{2}\right)^{\text{th}} term. If n is even, the median is the average of the two middle terms:
\text{Median} = \frac{1}{2}\left[katex display="true"]\left(\frac{n}{2}\right)^{\text{th}}\text{ term} + \left(\frac{n}{2}+1\right)^{\text{th}}\text{ term}\right[/katex]
Odd set. Find the median of 12, 7, 9, 15, 4, 11, 6, 13, 8. Arrange in ascending order: 4, 6, 7, 8, 9, 11, 12, 13, 15. Here n = 9, which is odd. The median is the 5th term, which is 9.
Even set. Find the median of 5, 8, 2, 11, 7, 14, 3, 9. Arrange: 2, 3, 5, 7, 8, 9, 11, 14. Here n = 8, which is even. The median is \frac{1}{2}(7 + 8) = 7.5.
Common mistake. Skipping the arrange step breaks the answer. The median depends on the order of the values. A quick check: the median should sit between the middle values after sorting, never before sorting.
Edge case. Replacing a single value can shift the median. Take the heights of 8 students: 145, 152, 148, 155, 160, 158, 147, 153. Arranged: 145, 147, 148, 152, 153, 155, 158, 160. With n = 8, the median is \frac{1}{2}(152 + 153) = 152.5. Replace 160 with 149. The new order is 145, 147, 148, 149, 152, 153, 155, 158. The median is now \frac{1}{2}(149 + 152) = 150.5. One value moved the median by 2 units.
Mean versus median. The mean uses every value, so one extreme number pulls it. The median only looks at the middle position, so outliers barely affect it. When a data set has extreme values, the median is the safer measure. For more chapters, browse the Class 9 ICSE Maths book.
What to practise from Mean and Median Class 9 ICSE
This ICSE Class 9 chapter has two exercise blocks. Work through them in the order given. EXERCISE 19(A) builds the mean skills first, and EXERCISE 19(C) then mixes in the median.
- EXERCISE 19(A) — 14 questions. These cover finding the mean, applying the five properties, correcting misread observations, and combining means of separate groups.
- EXERCISE 19(C) — 10 questions. These mix mean and median problems, including finding a missing value and showing that the sum of deviations is zero.
To see all subjects at this level, visit the Class 9 ICSE books collection. For the official syllabus, check the CISCE website.
Mean and Median Class 9 ICSE frequently asked questions
What does the mean and median class 9 icse chapter cover?
It covers the mean of ungrouped data, the five properties of the mean, and the median of a data set. You also learn to correct a mean when an observation is misread.
What is the mean formula in class 9 ICSE?
The mean of n observations is their sum divided by n. In symbols, \bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i. It is the same as the average.
How do I find the median in Class 9 ICSE when the number of observations is even?
Arrange the data first, then average the two middle terms. Use \frac{1}{2}\left[katex display="true"]\left(\frac{n}{2}\right)^{\text{th}}\text{ term} + \left(\frac{n}{2}+1\right)^{\text{th}}\text{ term}\right[/katex].
Why is the sum of deviations from the mean always zero in Class 9 ICSE?
Because the mean is the balancing point of the data. The negative deviations from values below the mean cancel the positive deviations from values above it.
What happens to the mean in Class 9 ICSE if each observation is increased by a constant?
The mean increases by that same constant. This is Property 2. The same logic applies to subtraction, multiplication, and division by a constant.
Reference: ICSE Class 9 Mathematics textbook material, chapter 19: Mean and Median — CISCE-aligned.