Math Problem Statement
The number of pages in each book on a shelf is shown below:
300, 220, 450, 410, 240, 330, 290, 310, 350, 280
Solution
To analyze the number of pages in the books on the shelf, we can calculate several basic statistics: mean (average), median, mode, range, and standard deviation.
Let's go through these calculations:
- Mean (Average): The sum of all pages divided by the total number of books.
- Median: The middle value when all numbers are arranged in ascending order.
- Mode: The most frequently occurring value (if any).
- Range: The difference between the largest and smallest values.
- Standard Deviation: A measure of how spread out the numbers are from the mean.
Let me calculate these for you.Here are the calculated statistics for the number of pages in the books:
- Mean (Average): 318 pages
- Median: 305 pages
- Mode: 220 pages
- Range: 230 pages (difference between the maximum and minimum values)
- Standard Deviation: 67.35 pages (approximately)
Would you like further details or have any questions about these statistics?
Here are five related questions:
- What would happen to the mean if you added another book with 500 pages?
- How would the median change if one of the middle books had 400 pages?
- If you remove the book with the fewest pages, what impact would this have on the range?
- How does standard deviation help in understanding the spread of pages in these books?
- Is it possible to have more than one mode? If so, how?
Tip: The median is a robust measure of central tendency, as it is less affected by extreme values than the mean.
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Math Problem Analysis
Mathematical Concepts
Descriptive Statistics
Formulas
Mean
Median
Mode
Range
Standard Deviation
Theorems
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Suitable Grade Level
Grades 7-9
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