Create a histogram for the number of pages in six books read by a student.

Check the final answer first, then review the worked steps.

Problem

Create a histogram for the number of pages in six books read by a student.

Answer

Histogram with bars representing frequencies for page ranges: [44, 179) with frequency 1, [179, 314) with frequency 3, [314, 449) with frequency 1, [449, 584] with frequency 1.

Step-by-step solution

  1. Identify the data: The number of pages in the six books read by Pedro are: 584, 201, 255, 44, 312, 334.
  1. Determine the range of the data: The minimum number of pages is 44 and the maximum is 584. The range is $584 - 44 = 540$.
  1. Choose the number of bins: A common guideline is to use the square root of the number of data points. Here, we have 6 data points, so $\sqrt{6} \approx 2.45$. We can round this up to 3 or 4 bins for a reasonable representation. Let's choose 4 bins for better detail.
  1. Determine the bin width: Divide the range by the number of bins: $\frac{540}{4} = 135$. So, each bin will cover a range of 135 pages.

5. Define the bin intervals: Starting from the minimum value, we create the bins:
- Bin 1: 44 - (44 + 135) = 44 - 179
- Bin 2: 179 - (179 + 135) = 179 - 314
- Bin 3: 314 - (314 + 135) = 314 - 449
- Bin 4: 449 - (449 + 135) = 449 - 584

6. Count the frequency for each bin:
- Bin 1 (44 - 179): 44 (1 book)
- Bin 2 (179 - 314): 201, 255, 312 (3 books)
- Bin 3 (314 - 449): 334 (1 book)
- Bin 4 (449 - 584): 584 (1 book)

  1. Create the histogram: The histogram will have the number of pages on the x-axis and the number of books (frequency) on the y-axis. Each bin will be represented by a bar whose height corresponds to its frequency.
  • The first bar will go from 44 to 179 on the x-axis, with a height of 1.
  • The second bar will go from 179 to 314 on the x-axis, with a height of 3.
  • The third bar will go from 314 to 449 on the x-axis, with a height of 1.
  • The fourth bar will go from 449 to 584 on the x-axis, with a height of 1.

The provided image shows an empty histogram. To complete it, you would draw these bars.