Class 9 Maths Chapter 12 Statistics – Exercise 12.1 NCERT Solutions

Introduction

Exercise 12.1 introduces basic statistical concepts such as mean, median, and mode of ungrouped data. Students learn how to calculate measures of central tendency and interpret them in real‑life contexts. This exercise builds the foundation for data handling and probability.

Key Concepts

1. Mean (Average):

$$\text{Mean}=\frac{\text{Sum of observations}}{\text{Number of observations}}$$

2. Median:

   • Arrange data in ascending order.

   • If $n$ is odd: median = middle value.

   • If $n$ is even: median = average of two middle values.

3. Mode: The observation occurring most frequently.

Common Mistakes

• Forgetting to arrange data before finding median.

• Confusing mean with median.

• Ignoring frequency of values when finding mode.

• Arithmetic errors in calculating averages.

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

Q1. Find mean of 5, 10, 15, 20, 25.

$$\text{Mean}=\frac{5+10+15+20+25}{5}=\frac{75}{5}=15$$

Q2. Find mean of 7, 14, 21, 28, 35.

$$\text{Mean}=\frac{7+14+21+28+35}{5}=\frac{105}{5}=21$$

Q3. Find mean of 2, 4, 6, 8, 10, 12.

$$\text{Mean}=\frac{42}{6}=7$$

Q4. Find median of 3, 5, 7, 9, 11. Odd number of terms → median = middle value = 7.

Q5. Find median of 2, 4, 6, 8, 10, 12. Even number of terms → median = average of middle two values = $\frac{6+8}{2}=7$.

Q6. Find mode of 2, 3, 3, 4, 5, 5, 5, 6. Mode = most frequent value = 5.

Q7. Find mode of 7, 8, 9, 9, 10, 11, 11, 11. Mode = 11.

Q8. Find mean, median, and mode of 1, 2, 2, 3, 4. Mean = $\frac{12}{5}=2.4$. Median = middle value = 2. Mode = most frequent value = 2.

Q9. Find mean, median, and mode of 6, 7, 8, 9, 10, 10, 11. Mean = $\frac{61}{7}=8.71$. Median = middle value = 9. Mode = 10.

Q10. Find mean, median, and mode of 12, 15, 17, 17, 18, 20, 22. Mean = $\frac{121}{7}=17.29$. Median = middle value = 17. Mode = 17.

FAQs (10)

FAQ1. What is mean? Average of all observations.

FAQ2. What is median? Middle value of arranged data.

FAQ3. What is mode? Most frequent observation.

FAQ4. Why arrange data for median? To identify middle value correctly.

FAQ5. Can mean, median, and mode be equal? Yes, in symmetric data sets.

FAQ6. What is practical use of mean? Used in calculating averages (marks, speed).

FAQ7. What is practical use of median? Used in finding middle income, middle age.

FAQ8. What is practical use of mode? Used in identifying most popular choice.

FAQ9. Why is Exercise 12.1 important? It introduces measures of central tendency.

FAQ10. What is unit of mean, median, mode? Same as unit of data values.

Conclusion

Exercise 12.1 covers mean, median, and mode of ungrouped data with solved examples and FAQs. Mastering these problems helps students understand basic statistics and apply them in real‑life situations.

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