Female undergraduate engineering students at ASU reported their heights to the nearest inch, as follows: 63, 62, 65, 65, 66, 69, 64, 68, 69, 68, 66, 61, 70, 65, 65, 68, 65, 67, 64, 70, 64, 64, 68, 69, 68, 67, 67, 63, 69, 62, 64, 70, 63, 64, 65, 65, 70. To construct a histogram of the female students' heights with 10 bins, follow these steps: 1. Calculate the range by subtracting the smallest height from the largest. 2. Divide the range by the number of bins (10) to get the bin width. 3. Create bins using the bin width and range. 4. Tally the number of heights in each bin. 5. Plot the histogram with the bins on the horizontal axis and the frequency on the vertical axis. 6. Label the axes and title the histogram. To draw the histogram, use graph paper, a computer with statistical software, or tools like Microsoft Excel or Google Sheets.

1. First, calculate the range by subtracting the smallest height (61 inches) from the largest (70 inches): 70 - 61 = 9 inches.

2. Next, divide the range by the number of bins, which is 10: 9 inches / 10 bins = 0.9 inches per bin. Generally, we round the bin width up to make it easier to work with, so let's use a bin width of 1 inch.

3. Now, create the bins using the bin width. Since we rounded the width to 1 inch, we will have bins that start at 61 and go up to 70, with each bin covering one inch. They will look like this: [61, 62), [62, 63), ... [69, 70), [70, 71).

4. Tally the heights into each bin: - [61, 62): 1 student (61) - [62, 63): 2 students (62, 62) - [63, 64): 3 students (63, 63, 63) - [64, 65): 8 students (64, 64, 64, 64, 64, 64, 64, 64) - [65, 66): 6 students (65, 65, 65, 65, 65, 65) - [66, 67): 2 students (66, 66) - [67, 68): 4 students (67, 67, 67, 67) - [68, 69): 6 students (68, 68, 68, 68, 68, 68) - [69, 70): 4 students (69, 69, 69, 69) - [70, 71): 4 students (70, 70, 70, 70)

5. Now you can plot the histogram with the information from step 4. For each bin, draw a bar that represents the number of students with heights in that bin. For instance, the bar for the bin [61, 62) will be 1 unit high, the bar for [62, 63) will be 2 units high, and so on.

6. Label the horizontal axis with the height bins and the vertical axis with the frequency, which is the number of students in each bin. At the top of the histogram, provide a title that represents what the graph is about, such as "Histogram of Female Undergraduate Engineering Student Heights at ASU".

Note that step 5 may be completed with the use of graph paper or digital tools like Excel or Google Sheets, which have histogram functions that can automate this process after inputting the data.

Extra:

A histogram is a graphical representation that organizes a group of data points into user-specified ranges. It is similar to a bar graph, but a histogram groups numbers into ranges (bins). The height of the bar shows how many fall into each range. And unlike a bar graph, the bars in a histogram touch each other to indicate that the range of data is continuous.

When creating bins for a histogram, it's important to decide on a range that makes sense for your data. Sometimes, the data will determine the bin edges for you (like in our case with heights to the nearest inch), but other times, you'll have to decide based on the distribution of the data. The important thing is that all bins must be of equal width.

Histograms are useful for showing the shape and spread of continuous sample data, and can help in understanding where the values lie within a range. By looking at a histogram, you can understand if the distribution is symmetric, skewed, has outliers, or distinct peaks. This information can be valuable in statistical analysis, like determining the average or median of the data, or in applying further statistical tests. For educational purposes, using a histogram to understand data forms a foundational skill in both mathematics and science, preparing students for more complex analysis techniques in various fields of study