Let's analyze the given data and answer each statement accordingly.
1. The mean number of cars sold in a month is the same at both dealerships.
To calculate the mean:
- Admiral Autos: [tex]\((4 + 19 + 15 + 10 + 17) / 5 = 65 / 5 = 13.0\)[/tex]
- Countywide Cars: [tex]\((9 + 17 + 14 + 10 + 15) / 5 = 65 / 5 = 13.0\)[/tex]
Since the mean for both dealerships is 13.0, this statement is supported by the data.
2. The median number of cars sold in a month is the same at both dealerships.
To find the median, we need to order the sales figures and find the middle value:
- Admiral Autos: Ordered list: [tex]\([4, 10, 15, 17, 19]\)[/tex]. The middle value is [tex]\(15\)[/tex].
- Countywide Cars: Ordered list: [tex]\([9, 10, 14, 15, 17]\)[/tex]. The middle value is [tex]\(14\)[/tex].
Since the medians are different, this statement is not supported by the data.
3. The total number of cars sold is the same at both dealerships.
To calculate the total:
- Admiral Autos: [tex]\(4 + 19 + 15 + 10 + 17 = 65\)[/tex]
- Countywide Cars: [tex]\(9 + 17 + 14 + 10 + 15 = 65\)[/tex]
Since the total number of cars sold at both dealerships is 65, this statement is supported by the data.
4. The range of the number of cars sold is the same for both dealerships.
To find the range, we calculate the difference between the highest and lowest values:
- Admiral Autos: Range [tex]\(= 19 - 4 = 15\)[/tex]
- Countywide Cars: Range [tex]\(= 17 - 9 = 8\)[/tex]
Since the ranges are different, this statement is not supported by the data.
5. The data for Admiral Autos shows greater variability.
To determine variability, we look at the standard deviations:
- Admiral Autos: Standard deviation [tex]\( \approx 5.40\)[/tex]
- Countywide Cars: Standard deviation [tex]\( \approx 3.03\)[/tex]
Since the standard deviation for Admiral Autos is higher, this statement is supported by the data.
Summary:
- The mean number of cars sold in a month is the same at both dealerships. (Supported)
- The median number of cars sold in a month is the same at both dealerships. (Not supported)
- The total number of cars sold is the same at both dealerships. (Supported)
- The range of the number of cars sold is the same for both dealerships. (Not supported)
- The data for Admiral Autos shows greater variability. (Supported)
Thus, the supported statements are:
- The mean number of cars sold in a month is the same at both dealerships.
- The total number of cars sold is the same at both dealerships.
- The data for Admiral Autos shows greater variability.
