Class 9 Maths Chapter 12 Statistics – Exercise 12.4 NCERT Solutions

Introduction

Exercise 12.4 focuses on median of grouped data. Students learn how to calculate the median using the median formula for frequency distributions. This exercise is important for understanding the central tendency of data and interpreting real‑life datasets.

Key Formula

For grouped data, median is calculated using:

$$\text{Median}=l+\left(\frac{\frac{n}{2}-C}{f}\right)\cdot h$$

Where:

• $l$ = lower limit of median class

• $n$ = total frequency ($\sum f_i$)

• $C$ = cumulative frequency before median class

• $f$ = frequency of median class

• $h$ = class size

Common Mistakes

• Forgetting to calculate cumulative frequencies.

• Not identifying the correct median class.

• Arithmetic errors in numerator and denominator.

• Confusing median with mean or mode.

NCERT Questions with Step‑by‑Step Solutions (10)

Q1. Find median of data: Class intervals 0–10, 10–20, 20–30, 30–40; frequencies 5, 7, 10, 8. Total frequency $n=30$. Median class = 20–30 (since cumulative frequency crosses 15). $l=20,h=10,f=10,C=12$.

$$\text{Median}=20+\left(\frac{15-12}{10}\right)\cdot 10=20+3=23$$

Q2. Find median of data: Class intervals 0–20, 20–40, 40–60, 60–80; frequencies 10, 15, 20, 5. $n=50$. Median class = 40–60 (cumulative frequency crosses 25). $l=40,h=20,f=20,C=25$.

$$\text{Median}=40+\left(\frac{25-25}{20}\right)\cdot 20=40$$

Q3. Find median of data: Class intervals 0–10, 10–20, 20–30; frequencies 3, 4, 5. $n=12$. Median class = 20–30 (cumulative frequency crosses 6). $l=20,h=10,f=5,C=7$.

$$\text{Median}=20+\left(\frac{6-7}{5}\right)\cdot 10=20-2=18$$

Q4. Find median of data: Class intervals 10–20, 20–30, 30–40, 40–50; frequencies 6, 8, 10, 6. $n=30$. Median class = 30–40 (cumulative frequency crosses 15). $l=30,h=10,f=10,C=14$.

$$\text{Median}=30+\left(\frac{15-14}{10}\right)\cdot 10=31$$

Q5. Find median of data: Class intervals 0–10, 10–20, 20–30, 30–40; frequencies 2, 6, 8, 4. $n=20$. Median class = 20–30 (cumulative frequency crosses 10). $l=20,h=10,f=8,C=8$.

$$\text{Median}=20+\left(\frac{10-8}{8}\right)\cdot 10=22.5$$

Q6. Find median of data: Class intervals 0–20, 20–40, 40–60; frequencies 5, 10, 15. $n=30$. Median class = 40–60 (cumulative frequency crosses 15). $l=40,h=20,f=15,C=15$.

$$\text{Median}=40+\left(\frac{15-15}{15}\right)\cdot 20=40$$

Q7. Find median of data: Class intervals 10–30, 30–50, 50–70; frequencies 7, 9, 4. $n=20$. Median class = 30–50 (cumulative frequency crosses 10). $l=30,h=20,f=9,C=7$.

$$\text{Median}=30+\left(\frac{10-7}{9}\right)\cdot 20=36.67$$

Q8. Find median of data: Class intervals 0–25, 25–50, 50–75, 75–100; frequencies 5, 10, 15, 20. $n=50$. Median class = 50–75 (cumulative frequency crosses 25). $l=50,h=25,f=15,C=15$.

$$\text{Median}=50+\left(\frac{25-15}{15}\right)\cdot 25=66.67$$

Q9. Find median of data: Class intervals 0–10, 10–20, 20–30, 30–40, 40–50; frequencies 4, 6, 8, 10, 12. $n=40$. Median class = 30–40 (cumulative frequency crosses 20). $l=30,h=10,f=10,C=18$.

$$\text{Median}=30+\left(\frac{20-18}{10}\right)\cdot 10=32$$

Q10. Find median of data: Class intervals 0–20, 20–40, 40–60, 60–80; frequencies 8, 12, 20, 10. $n=50$. Median class = 40–60 (cumulative frequency crosses 25). $l=40,h=20,f=20,C=20$.

$$\text{Median}=40+\left(\frac{25-20}{20}\right)\cdot 20=45$$

FAQs (10)

FAQ1. What is median? Middle value of dataset.

FAQ2. What is median class? Class interval containing the middle observation.

FAQ3. Why calculate cumulative frequency? To identify median class.

FAQ4. What is class size? Difference between upper and lower class limits.

FAQ5. Can median be unique? Yes, for a given dataset.

FAQ6. Can mean, median, and mode be equal? Yes, in symmetric distributions.

FAQ7. Why is Exercise 12.4 important? It teaches calculation of median for grouped data.

FAQ8. What is unit of median? Same as unit of data values.

FAQ9. What is practical use of median? Used in finding middle income, middle age, etc.

FAQ10. What is difference between mean and median? Mean = average, Median = middle value.

Conclusion

Exercise 12.4 covers median of grouped data with solved examples and FAQs. Mastering these problems helps students analyze frequency distributions and apply statistics in real‑life contexts.

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