Question
Georgina likes to read during her summer break. The table below shows the number of pages in each book she read last summer and the number of pages in each book she read this summer.
Number of Pages Georgina Reads during the Summer
Last Summer
140
220
190
180
190
This Summer
150
170
150
190
180
What inference can someone draw about the data?
The books she read this summer had more pages, on average, than last summer.
The number of pages in each book varied more last summer than this summer.
Last summer, the average book had nearly twice the number of pages than the average book has this summer.
This summer, the number of pages in a book varied nearly twice as much as the number of pages in last summer's books
Number of Pages Georgina Reads during the Summer
Last Summer
140
220
190
180
190
This Summer
150
170
150
190
180
What inference can someone draw about the data?
The books she read this summer had more pages, on average, than last summer.
The number of pages in each book varied more last summer than this summer.
Last summer, the average book had nearly twice the number of pages than the average book has this summer.
This summer, the number of pages in a book varied nearly twice as much as the number of pages in last summer's books
Answers
GPT-4o mini
To draw conclusions from the data, let's first calculate the average number of pages for each summer and analyze the variation.
**Last Summer:**
- Books: 140, 220, 190, 180, 190
- Total pages: 140 + 220 + 190 + 180 + 190 = 1,110
- Average pages: 1,110 / 5 = 222 pages (this is incorrect; let's recalculate)
Total: 140 + 220 + 190 + 180 + 190 = 1,110
Average pages: 1,110 / 5 = **222 pages**
**This Summer:**
- Books: 150, 170, 150, 190, 180
- Total pages: 150 + 170 + 150 + 190 + 180 = 1,040
- Average pages: 1,040 / 5 = 208 pages
Total: 150 + 170 + 150 + 190 + 180 = 1,040
Average pages: 1,040 / 5 = **208 pages**
**Summary of Averages:**
- Average from last summer = 190 pages
- Average from this summer = 164 pages
Now let's evaluate the options provided:
1. **The books she read this summer had more pages, on average, than last summer.**
- This is false, as the average pages were higher last summer (190) than this summer (164).
2. **The number of pages in each book varied more last summer than this summer.**
- To analyze this, we need the range or standard deviation.
- Last Summer: Range = 220 - 140 = 80
- This Summer: Range = 190 - 150 = 40
- This statement seems to be true since the range of pages was larger last summer.
3. **Last summer, the average book had nearly twice the number of pages than the average book has this summer.**
- This is not true, the average pages are 190 and 164, which is not double.
4. **This summer, the number of pages in a book varied nearly twice as much as the number of pages in last summer's books.**
- This is not true since the range this summer was 40 pages, while last summer's variation was 80 pages.
Therefore, the correct inference based on the data is:
**The number of pages in each book varied more last summer than this summer.**
**Last Summer:**
- Books: 140, 220, 190, 180, 190
- Total pages: 140 + 220 + 190 + 180 + 190 = 1,110
- Average pages: 1,110 / 5 = 222 pages (this is incorrect; let's recalculate)
Total: 140 + 220 + 190 + 180 + 190 = 1,110
Average pages: 1,110 / 5 = **222 pages**
**This Summer:**
- Books: 150, 170, 150, 190, 180
- Total pages: 150 + 170 + 150 + 190 + 180 = 1,040
- Average pages: 1,040 / 5 = 208 pages
Total: 150 + 170 + 150 + 190 + 180 = 1,040
Average pages: 1,040 / 5 = **208 pages**
**Summary of Averages:**
- Average from last summer = 190 pages
- Average from this summer = 164 pages
Now let's evaluate the options provided:
1. **The books she read this summer had more pages, on average, than last summer.**
- This is false, as the average pages were higher last summer (190) than this summer (164).
2. **The number of pages in each book varied more last summer than this summer.**
- To analyze this, we need the range or standard deviation.
- Last Summer: Range = 220 - 140 = 80
- This Summer: Range = 190 - 150 = 40
- This statement seems to be true since the range of pages was larger last summer.
3. **Last summer, the average book had nearly twice the number of pages than the average book has this summer.**
- This is not true, the average pages are 190 and 164, which is not double.
4. **This summer, the number of pages in a book varied nearly twice as much as the number of pages in last summer's books.**
- This is not true since the range this summer was 40 pages, while last summer's variation was 80 pages.
Therefore, the correct inference based on the data is:
**The number of pages in each book varied more last summer than this summer.**