NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.1Question 7
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.1
Question. 7
Consider the distribution:
| Class | 0–5 | 6–11 | 12–17 | 18–23 | 24–29 |
|---|---|---|---|---|---|
| Frequency | 13 | 10 | 15 | 8 | 11 |
The upper limit of the median class is
(A)
17
(B)
17.5
(C)
18
(D)
18.5
Detailed Answer with Explanation:
Step 1: First, add up all the frequencies to get the total number of observations (N).
\(N = 13 + 10 + 15 + 8 + 11 = 57\)
Step 2: Find \(N/2\).
\(N/2 = 57/2 = 28.5\)
Step 3: Make the cumulative frequencies (keep adding one by one).
- For 0–5: \(13\)
- For 6–11: \(13 + 10 = 23\)
- For 12–17: \(23 + 15 = 38\)
- For 18–23: \(38 + 8 = 46\)
- For 24–29: \(46 + 11 = 57\)
Step 4: Now check where \(28.5\) lies in the cumulative frequencies.
It is greater than 23 but less than or equal to 38. So, the median class is 12–17.
Step 5: The upper limit of this class (12–17) is 17.
Final Answer: The upper limit of the median class is 17. So, option (A) is correct.