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Answer :
Let's solve this problem step by step by analyzing the effect of adding the integer 10 to data set F to create data set G:
1. Understanding the Data Sets:
- Data set F consists of 55 integers, all between 170 and 290.
- Data set G consists of all integers in data set F plus an additional integer 10.
2. Effect on the Mean:
- The mean is the average of all numbers in a data set.
- Since all numbers in data set F are between 170 and 290, adding the integer 10 (which is smaller than any number in F) to create data set G will decrease the overall average.
- Therefore, the mean of data set G will be less than the mean of data set F.
3. Effect on the Median:
- The median is the middle value of a data set when the numbers are arranged in order.
- For data set F with 55 numbers, the median would be approximately the 28th value in the ordered list.
- When you add 10 to create data set G, there are 56 numbers. In an ordered list, 10 will be the smallest number and likely be near the beginning.
- The new median for data set G would be the average of the 28th and 29th values in the ordered list of G. Since 10 has no effect on these positions, the overall range (170 to 290) remains dominant in determining the median.
- Therefore, adding a very small number like 10 doesn't significantly affect the median, as it is focused on the center of the data distribution.
Based on this analysis, the correct answer is:
A. I only (The mean must be less for data set F than for data set G, while the median is unaffected by the addition of 10).
1. Understanding the Data Sets:
- Data set F consists of 55 integers, all between 170 and 290.
- Data set G consists of all integers in data set F plus an additional integer 10.
2. Effect on the Mean:
- The mean is the average of all numbers in a data set.
- Since all numbers in data set F are between 170 and 290, adding the integer 10 (which is smaller than any number in F) to create data set G will decrease the overall average.
- Therefore, the mean of data set G will be less than the mean of data set F.
3. Effect on the Median:
- The median is the middle value of a data set when the numbers are arranged in order.
- For data set F with 55 numbers, the median would be approximately the 28th value in the ordered list.
- When you add 10 to create data set G, there are 56 numbers. In an ordered list, 10 will be the smallest number and likely be near the beginning.
- The new median for data set G would be the average of the 28th and 29th values in the ordered list of G. Since 10 has no effect on these positions, the overall range (170 to 290) remains dominant in determining the median.
- Therefore, adding a very small number like 10 doesn't significantly affect the median, as it is focused on the center of the data distribution.
Based on this analysis, the correct answer is:
A. I only (The mean must be less for data set F than for data set G, while the median is unaffected by the addition of 10).
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