Question 1200043: The flowing data is organized by using a stem-and lead displays for the weights of 10 people
Stems Leaves
5 0 2
6 2 4 4
7 1 5 5 5
8 8
Based on the above data:
a) Develop the frequency distribution table
b) Show on the table the relative frequently distribution and percent frequency distribution for each group
c) Calculate the mean
d) Calculate 1 percent of trimmed mean
e) Calculate the weighted mean
f) Calculate median
g) Calculate the mode
h) Calculate the range
i) Find the first, second and third quartile
j) Calculate the 80th percentile and interpret the results obtained
Answer by textot(100)   (Show Source):
You can put this solution on YOUR website! **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.
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