9. Distribution of weights (kg) of 40 persons:
| Weight (kg) | 40–45 | 45–50 | 50–55 | 55–60 | 60–65 | 65–70 | 70–75 | 75–80 |
|---|---|---|---|---|---|---|---|---|
| No. of persons | 4 | 4 | 13 | 5 | 6 | 5 | 2 | 1 |
Construct the less-than type cumulative frequency table.
| Less than | 45 | 50 | 55 | 60 | 65 | 70 | 75 | 80 |
|---|---|---|---|---|---|---|---|---|
| Cumulative frequency | 4 | 8 | 21 | 26 | 32 | 37 | 39 | 40 |
Step 1: Look at the given table. The weights are divided into groups (called class intervals) like 40–45, 45–50, 50–55, etc. The number of persons in each group is given below it.
Step 2: In a less-than cumulative frequency table, we keep adding the frequencies step by step. For each class, we take "less than upper value".
Step 3: Start with the first class (40–45). - Upper value = 45 - No. of persons in this class = 4 - So, less than 45 → cumulative frequency = 4.
Step 4: Next class (45–50). - Upper value = 50 - Persons in this class = 4 - Add to previous cumulative (4 + 4 = 8) - So, less than 50 → cumulative frequency = 8.
Step 5: Next class (50–55). - Upper value = 55 - Persons in this class = 13 - Add to previous cumulative (8 + 13 = 21) - So, less than 55 → cumulative frequency = 21.
Step 6: Next class (55–60). - Upper value = 60 - Persons in this class = 5 - Add to previous cumulative (21 + 5 = 26) - So, less than 60 → cumulative frequency = 26.
Step 7: Next class (60–65). - Upper value = 65 - Persons in this class = 6 - Add to previous cumulative (26 + 6 = 32) - So, less than 65 → cumulative frequency = 32.
Step 8: Next class (65–70). - Upper value = 70 - Persons in this class = 5 - Add to previous cumulative (32 + 5 = 37) - So, less than 70 → cumulative frequency = 37.
Step 9: Next class (70–75). - Upper value = 75 - Persons in this class = 2 - Add to previous cumulative (37 + 2 = 39) - So, less than 75 → cumulative frequency = 39.
Step 10: Last class (75–80). - Upper value = 80 - Persons in this class = 1 - Add to previous cumulative (39 + 1 = 40) - So, less than 80 → cumulative frequency = 40.
Step 11: Write all values in a new table as shown in the answer. This is the less-than type cumulative frequency table.