Question
Here's are the prices for biweekly lawn mowing services for local companies 15 15 20 30 35 40 40 50 50 50 which measure of center mean or medium best represents the shape of the distribution A medium the shape of the distribution is skewed to the right B median the shape of the distribution skewed to the left C Nina the shape of the distribution is skew to the left D mean the shape of the distribution is close to symmetrical
Answers
GPT-4o mini
To analyze which measure of center (mean or median) best represents the shape of the distribution of the given lawn mowing prices, let's first look at the data you provided:
15, 15, 20, 30, 35, 40, 40, 50, 50, 50.
### 1. **Calculate the Mean:**
- Sum of the data: \(15 + 15 + 20 + 30 + 35 + 40 + 40 + 50 + 50 + 50 = 350\)
- Number of data points: \(10\)
- Mean: \(\frac{350}{10} = 35\)
### 2. **Calculate the Median:**
- To find the median, we need to arrange the data in order (which is already done):
15, 15, 20, 30, 35, 40, 40, 50, 50, 50
- Since there are 10 data points (an even number), the median is the average of the 5th and 6th values:
- 5th value = 35
- 6th value = 40
- Median: \(\frac{35 + 40}{2} = 37.5\)
### 3. **Shape of the Distribution:**
- **Visual Look**: The data points include several lower values (15s and 20) with a group around 40 and 50, and a limited number of high values (35, 40, 50). While the data is not extremely skewed, there is a clustering of higher-valued data points.
- **Skewness**: Since there are lower values, the distribution could be considered slightly skewed to the **right** because the higher values (50) might potentially influence the mean more than the median.
### Conclusion:
Given that the distribution is slightly skewed to the right and that the median (37.5) is less affected by the higher end of the data compared to the mean (35), the median would be a better measure of center to represent this distribution.
### Therefore, the correct answer is:
**A: Median, the shape of the distribution is skewed to the right.**
15, 15, 20, 30, 35, 40, 40, 50, 50, 50.
### 1. **Calculate the Mean:**
- Sum of the data: \(15 + 15 + 20 + 30 + 35 + 40 + 40 + 50 + 50 + 50 = 350\)
- Number of data points: \(10\)
- Mean: \(\frac{350}{10} = 35\)
### 2. **Calculate the Median:**
- To find the median, we need to arrange the data in order (which is already done):
15, 15, 20, 30, 35, 40, 40, 50, 50, 50
- Since there are 10 data points (an even number), the median is the average of the 5th and 6th values:
- 5th value = 35
- 6th value = 40
- Median: \(\frac{35 + 40}{2} = 37.5\)
### 3. **Shape of the Distribution:**
- **Visual Look**: The data points include several lower values (15s and 20) with a group around 40 and 50, and a limited number of high values (35, 40, 50). While the data is not extremely skewed, there is a clustering of higher-valued data points.
- **Skewness**: Since there are lower values, the distribution could be considered slightly skewed to the **right** because the higher values (50) might potentially influence the mean more than the median.
### Conclusion:
Given that the distribution is slightly skewed to the right and that the median (37.5) is less affected by the higher end of the data compared to the mean (35), the median would be a better measure of center to represent this distribution.
### Therefore, the correct answer is:
**A: Median, the shape of the distribution is skewed to the right.**