Question
City Price
Boston $125
Atlanta $50
New Orleans $38
Houston $44
Denver $49
Salt Lake City $45
Jenna writes a fashion blog. Recently, she researched the prices around the country for a popular pair of jeans. She wants to share the prices with her readers in a meaningful way by using the BEST measure of central tendency. Using the table's data, which statements are correct for this situation?
Responses
A The median is $47.The median is $47.
B The mean is $58.50.The mean is $58.50.
C The mean is the best measure to describe the data.The mean is the best measure to describe the data.
D The median is the best measure to describe the data.The median is the best measure to describe the data.
E The outlier, $125, affects the median more than the mean.
Answers
GPT-4o mini
To analyze Jenna's data and determine the best measure of central tendency, let's first compute the mean and median of the prices.
The prices are as follows:
- Boston: $125
- Atlanta: $50
- New Orleans: $38
- Houston: $44
- Denver: $49
- Salt Lake City: $45
### Step 1: Calculate the Mean
The mean is calculated by summing all the prices and dividing by the number of prices.
Sum of prices = $125 + $50 + $38 + $44 + $49 + $45 = $351
Number of prices = 6
Mean = Total Sum / Number of Prices = $351 / 6 = $58.50
### Step 2: Calculate the Median
To find the median, we first need to order the prices from lowest to highest:
- New Orleans: $38
- Houston: $44
- Salt Lake City: $45
- Atlanta: $50
- Denver: $49
- Boston: $125
With an even number of observations (6), the median is the average of the two middle values (the 3rd and 4th values in the ordered list).
The 3rd value (Salt Lake City) = $45
The 4th value (Atlanta) = $50
Median = ($45 + $50) / 2 = $95 / 2 = $47.5
### Step 3: Analyze Statements
Now, we will evaluate the statements:
A. **The median is $47.** - **Incorrect.** The median we calculated is $47.5.
B. **The mean is $58.50.** - **Correct.** This is the correct mean.
C. **The mean is the best measure to describe the data.** - **Incorrect.** The presence of the outlier ($125) skews the mean higher; the median is generally preferred in skewed distributions.
D. **The median is the best measure to describe the data.** - **Correct.** As discussed above, the median is less affected by the outlier and is a better measure for this dataset.
E. **The outlier, $125, affects the median more than the mean.** - **Incorrect.** The outlier has a larger effect on the mean than the median.
### Conclusion
The correct statements in this situation are:
- **B. The mean is $58.50.**
- **D. The median is the best measure to describe the data.**
The prices are as follows:
- Boston: $125
- Atlanta: $50
- New Orleans: $38
- Houston: $44
- Denver: $49
- Salt Lake City: $45
### Step 1: Calculate the Mean
The mean is calculated by summing all the prices and dividing by the number of prices.
Sum of prices = $125 + $50 + $38 + $44 + $49 + $45 = $351
Number of prices = 6
Mean = Total Sum / Number of Prices = $351 / 6 = $58.50
### Step 2: Calculate the Median
To find the median, we first need to order the prices from lowest to highest:
- New Orleans: $38
- Houston: $44
- Salt Lake City: $45
- Atlanta: $50
- Denver: $49
- Boston: $125
With an even number of observations (6), the median is the average of the two middle values (the 3rd and 4th values in the ordered list).
The 3rd value (Salt Lake City) = $45
The 4th value (Atlanta) = $50
Median = ($45 + $50) / 2 = $95 / 2 = $47.5
### Step 3: Analyze Statements
Now, we will evaluate the statements:
A. **The median is $47.** - **Incorrect.** The median we calculated is $47.5.
B. **The mean is $58.50.** - **Correct.** This is the correct mean.
C. **The mean is the best measure to describe the data.** - **Incorrect.** The presence of the outlier ($125) skews the mean higher; the median is generally preferred in skewed distributions.
D. **The median is the best measure to describe the data.** - **Correct.** As discussed above, the median is less affected by the outlier and is a better measure for this dataset.
E. **The outlier, $125, affects the median more than the mean.** - **Incorrect.** The outlier has a larger effect on the mean than the median.
### Conclusion
The correct statements in this situation are:
- **B. The mean is $58.50.**
- **D. The median is the best measure to describe the data.**