Question 1192782: . The table below shows the frequency distribution of the masses of 52 female students at a college. Measurements have been recorded to the nearest Kilogram Mass (Kg) Frequency 40-44 3 45-49 2 50-54 7 55-59 18 60-64 18 65-69 3 70-74 1
i. Construct a cumulative frequency table and draw a cumulative frequency curve ii. How many students weighed less than 57Kg?
iii. How many students weighed more than 61Kg?
iv. 20% were heavier than x Kg. Find the value of
v. Estimate the median
vi. Estimate the interquartile range 4. The frequency distribution shows the number of
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! **i. Construct a Cumulative Frequency Table:**
| Mass (Kg) | Frequency | Cumulative Frequency |
|---|---|---|
| 40-44 | 3 | 3 |
| 45-49 | 2 | 5 |
| 50-54 | 7 | 12 |
| 55-59 | 18 | 30 |
| 60-64 | 18 | 48 |
| 65-69 | 3 | 51 |
| 70-74 | 1 | 52 |
**ii. How many students weighed less than 57Kg?**
* From the cumulative frequency table, we see that 30 students weighed less than 57Kg.
**iii. How many students weighed more than 61Kg?**
* Total students = 52
* Students weighing less than or equal to 61Kg = 48 (from the cumulative frequency table)
* Students weighing more than 61Kg = Total students - Students weighing less than or equal to 61Kg = 52 - 48 = 4 students
**iv. 20% were heavier than x Kg. Find the value of x**
* 20% of the students = 0.20 * 52 = 10.4 students
* Since we are dealing with whole numbers, we can round up to 11 students.
* From the cumulative frequency table, we can see that 41 students weigh less than or equal to 64Kg.
* Therefore, 52 - 41 = 11 students weigh more than 64Kg.
* Hence, x = 64Kg
**v. Estimate the median**
* Median is the middle value when the data is arranged in ascending order.
* Since there are 52 students, the median lies between the 26th and 27th student.
* From the cumulative frequency table, we see that the 26th and 27th students fall within the 55-59Kg class.
* **Therefore, the estimated median lies within the 55-59Kg class.**
**vi. Estimate the interquartile range**
* **Find the first quartile (Q1):**
* 25% of 52 students = 13 students
* Q1 lies within the 50-54Kg class.
* **Find the third quartile (Q3):**
* 75% of 52 students = 39 students
* Q3 lies within the 60-64Kg class.
* **Estimate the interquartile range (IQR):**
* IQR = Q3 - Q1
* IQR ≈ (Upper limit of 60-64Kg class - Lower limit of 50-54Kg class)
* IQR ≈ 64.5 - 49.5 = 15Kg
**Note:** These are estimates based on the grouped data. For more precise calculations, you would need the individual weight measurements of each student.
I hope this helps! Let me know if you have any other questions.
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