Question 1200043
**a) Frequency Distribution Table**

| Weight (kg) | Frequency (f) |
|---|---|
| 50 | 2 |
| 52 | 1 |
| 62 | 1 |
| 64 | 2 |
| 71 | 1 |
| 75 | 3 |
| 88 | 1 |
| **Total** | **10** |

**b) Relative and Percent Frequency Distribution**

| Weight (kg) | Frequency (f) | Relative Frequency (f/n) | Percent Frequency (%) |
|---|---|---|---|
| 50 | 2 | 2/10 = 0.20 | 20% |
| 52 | 1 | 1/10 = 0.10 | 10% |
| 62 | 1 | 1/10 = 0.10 | 10% |
| 64 | 2 | 2/10 = 0.20 | 20% |
| 71 | 1 | 1/10 = 0.10 | 10% |
| 75 | 3 | 3/10 = 0.30 | 30% |
| 88 | 1 | 1/10 = 0.10 | 10% |
| **Total** | **10** | **1.00** | **100%** |

**c) Mean**

* **Calculate the sum of all weights:** 
   * 50 + 52 + 62 + 64 + 64 + 71 + 75 + 75 + 75 + 88 = 672 
* **Divide the sum of weights by the number of observations (n = 10):**
   * Mean = 672 / 10 = **67.2 kg**

**d) 1% Trimmed Mean**

* **Remove 1% of data from both ends:** 
   * Remove the lowest weight (50 kg) and the highest weight (88 kg).
* **Calculate the mean of the remaining 8 values:**
   * Sum of remaining weights: 52 + 62 + 64 + 64 + 71 + 75 + 75 + 75 = 533
   * Trimmed Mean = 533 / 8 = **66.625 kg**

**e) Weighted Mean (Not applicable in this case)**

* A weighted mean is used when different data points have different weights or importance. Since all weights in this dataset have equal importance, a simple mean is sufficient.

**f) Median**

* **Arrange the data in ascending order:** 
   * 50, 52, 62, 64, 64, 71, 75, 75, 75, 88
* **Find the middle value:** 
   * Since there are 10 observations (an even number), the median is the average of the 5th and 6th values:
      * Median = (64 + 71) / 2 = **67.5 kg**

**g) Mode**

* **The mode is the most frequent value:**
   * **Mode = 75 kg** (occurs 3 times)

**h) Range**

* **Range = Maximum value - Minimum value**
   * Range = 88 kg - 50 kg = **38 kg**

**i) Quartiles**

* **First Quartile (Q1):** 
   * Median of the lower half of the data (excluding the median if the number of data points is odd).
      * Lower half: 50, 52, 62, 64, 64 
      * Q1 = 62 kg
* **Second Quartile (Q2):** 
   * Median of the data (already calculated) 
      * Q2 = 67.5 kg
* **Third Quartile (Q3):** 
   * Median of the upper half of the data (excluding the median if the number of data points is odd).
      * Upper half: 71, 75, 75, 75, 88 
      * Q3 = 75 kg

**j) 80th Percentile**

* **The 80th percentile is the value below which 80% of the data falls.**
* **Find the position of the 80th percentile:** 
   * Position = (80/100) * n = 0.80 * 10 = 8th position
* **The 80th percentile is the 8th value in the ordered data:**
   * 80th percentile = 75 kg

**Interpretation of 80th Percentile:** 
80% of the people in the sample weigh 75 kg or less.