ICSE Class 10 Maths Chapter 24 Central Tendency Solutions
ICSE Class 10 Maths Chapter 24 central tendency solutions
ICSE Class 10 Maths Chapter 24 in Selina Concise Mathematics covers measures of central tendency: mean, median, quartiles and mode. This page gives formula notes and original step-by-step solutions for the main Chapter 24 question types, without inventing unsupported exercise counts, page numbers, marks or dates.
What this chapter tests
In Concise Mathematics Selina Solutions Class 10 ICSE Chapter 24 Measures of Central Tendency (Mean, Median, Quartiles and Mode), the key skill is choosing the correct method. Raw data must be arranged for median and quartiles. Frequency data needs columns such as fx, u or cumulative frequency. Grouped data needs the correct median class or modal class before substitution.
Edition note: Selina exercise numbering may vary by edition. The solutions below are Chapter 24 model solutions written in ICSE style, so they can be used to solve the matching textbook questions without relying on unsupported question-count claims.
Formula reference
| Topic | Formula | When to use |
|---|---|---|
| Mean | \bar{x}=\dfrac{\sum fx}{\sum f} | Use for a frequency distribution. |
| Step-deviation mean | \bar{x}=A+h\dfrac{\sum fu}{\sum f}, where u=\dfrac{x-A}{h} | Use when values have a common step h. |
| Grouped median | \text{Median}=l+\left(\dfrac{\frac{N}{2}-cf}{f}\right)h | Use after finding the median class. |
| Grouped mode | \text{Mode}=l+\dfrac{f_1-f_0}{2f_1-f_0-f_2}\times h | Use after finding the modal class. |
Here N=\sum f, cf is the cumulative frequency before the median class, l is the lower limit used in the class formula and h is the class width.
Concept snapshot
Think of data as students standing in a line. The mean shares the total equally. The median is the middle student after arranging the line. The mode is the value seen most often. Quartiles split the arranged line into four parts.
Mean worked solution
Mean questions usually ask for an average, a missing value or a shortcut method such as step-deviation.
Worked example 1: Mean by step-deviation
Question: Find the mean of the following distribution, correct to one decimal place.
| x | 10 | 15 | 20 | 25 | 30 |
|---|---|---|---|---|---|
| f | 3 | 5 | 9 | 7 | 6 |
Step 1: Take A=20 and h=5. Then u=\dfrac{x-A}{h}.
| x | f | u | fu |
|---|---|---|---|
| 10 | 3 | -2 | -6 |
| 15 | 5 | -1 | -5 |
| 20 | 9 | 0 | 0 |
| 25 | 7 | 1 | 7 |
| 30 | 6 | 2 | 12 |
| Total | \sum f=30 | \sum fu=8 |
Step 2: Substitute in the formula.
\bar{x}=A+h\dfrac{\sum fu}{\sum f}
\bar{x}=20+5\left(\dfrac{8}{30}\right)=21.333\ldots
Final answer: \bar{x}=21.3.
Median and quartiles worked solution
Median and quartiles are position-based. Always arrange raw observations before finding Q_1, Q_2 and Q_3.
Worked example 2: Median and quartiles
Question: Find Q_1, Q_2 and Q_3 for 20,12,30,15,36,22,18,27,14,25,34.
Step 1: Arrange the data in ascending order.
12,\ 14,\ 15,\ 18,\ 20,\ 22,\ 25,\ 27,\ 30,\ 34,\ 36
Step 2: Since n=11, the median position is \dfrac{n+1}{2}.
\dfrac{11+1}{2}=6
Step 3: The 6th observation is 22, so Q_2=22.
Step 4: The lower half is 12,14,15,18,20. Its middle value is 15, so Q_1=15.
Step 5: The upper half is 25,27,30,34,36. Its middle value is 30, so Q_3=30.
Final answer: Q_1=15,\ Q_2=22,\ Q_3=30.
Mode worked solution
For grouped data, the modal class is the class interval with the highest frequency.
Worked example 3: Mode of grouped data
Question: Find the mode for class intervals 0-10,10-20,20-30,30-40,40-50 with frequencies 5,8,12,9,6.
Step 1: The highest frequency is 12, so the modal class is 20-30.
Step 2: Use l=20,\ h=10,\ f_1=12,\ f_0=8,\ f_2=9.
\text{Mode}=l+\dfrac{f_1-f_0}{2f_1-f_0-f_2}\times h
\text{Mode}=20+\dfrac{12-8}{2(12)-8-9}\times 10
\text{Mode}=20+\dfrac{4}{7}\times 10=25.714\ldots
Final answer: Mode =25.7, correct to one decimal place.
Quick answer index
| Worked example | Type | Answer |
|---|---|---|
| 1 | Step-deviation mean | \bar{x}=21.3 |
| 2 | Quartiles | Q_1=15,\ Q_2=22,\ Q_3=30 |
| 3 | Grouped mode | \text{Mode}=25.7 |
Examiner’s mindset
For ICSE Class 10 Maths statistics answers, show the formula, the table columns and the substitution. In grouped median or mode, state the selected class before using the formula. A correct final value with no working is weaker than a clear method with labelled steps.
Common mistakes
- Using \sum x instead of \sum fx: In a frequency table, multiply first.
- Not arranging data: Median and quartiles need ascending order.
- Choosing the wrong modal class: Pick the class with highest frequency.
- Rounding early: Round only in the final answer when asked.
Related resources
For more practice, use ICSE Class 10 textbook solutions, ICSE textbook solutions and ICSE Class 10 Maths study resources. For official syllabus confirmation, check the CISCE website.
Frequently asked questions
Which formulas are needed for ICSE Class 10 Maths central tendency questions?
Learn \bar{x}=\frac{\sum fx}{\sum f}, the grouped median formula, the grouped mode formula, and the position method for Q_1, Q_2 and Q_3.
How do I choose the mean method?
Use direct mean for small values. Use assumed mean or step-deviation when values are large or have a common step, because the deviation column reduces calculation.
What is the difference between median and mode?
Median is the middle value after arranging data. Mode is the value or class with the highest frequency.
Should I round answers in Chapter 24?
Round only when the question asks for it. Keep exact working until the final line.
Sources used
- CISCE official website and syllabus publications
- CISCE ICSE Class X Mathematics syllabus publication page
- Selina Concise Mathematics Class 10, Chapter 24: Measures of Central Tendency (Mean, Median, Quartiles and Mode)
- NCERT mathematics textbook resources for standard statistics terminology