NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.3Question 13
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.3
Question. 13
13. Ages (years) of 300 patients on a day:
| Age | 10–20 | 20–30 | 30–40 | 40–50 | 50–60 | 60–70 |
|---|---|---|---|---|---|---|
| No. of patients | 60 | 42 | 55 | 70 | 53 | 20 |
Form (i) Less-than type and (ii) More-than type cumulative frequency distributions.
Answer:
(i) Less-than type
| Less than | 20 | 30 | 40 | 50 | 60 | 70 |
|---|---|---|---|---|---|---|
| CF | 60 | 102 | 157 | 227 | 280 | 300 |
(ii) More-than type
| More than or equal to | 10 | 20 | 30 | 40 | 50 | 60 | 70 |
|---|---|---|---|---|---|---|---|
| CF | 300 | 240 | 198 | 143 | 73 | 20 | 0 |
Detailed Answer with Explanation:
Step 1: Understand the data.
The table gives us age groups (class intervals) of patients and how many patients are in each group (frequency).
Step 2: Less-than type cumulative frequency.
- For "less than 20": Only the first group (10–20) is included. So CF = 60.
- For "less than 30": Add patients in 10–20 and 20–30 → 60 + 42 = 102.
- For "less than 40": Add one more group → 102 + 55 = 157.
- For "less than 50": Add one more group → 157 + 70 = 227.
- For "less than 60": Add one more group → 227 + 53 = 280.
- For "less than 70": Add the last group → 280 + 20 = 300.
Step 3: More-than type cumulative frequency.
- Start with total patients = 300.
- For "more than or equal to 20": Subtract the first group (10–20) → 300 – 60 = 240.
- For "more than or equal to 30": Subtract next group (20–30) → 240 – 42 = 198.
- For "more than or equal to 40": Subtract next group (30–40) → 198 – 55 = 143.
- For "more than or equal to 50": Subtract next group (40–50) → 143 – 70 = 73.
- For "more than or equal to 60": Subtract next group (50–60) → 73 – 53 = 20.
- For "more than or equal to 70": Subtract last group (60–70) → 20 – 20 = 0.
Step 4: Final tables.
We now have both cumulative frequency distributions as shown above.
This method works by step-by-step addition for "less than type" and subtraction from the total for "more than type".