Histograms

Subject Areas

Tools / Misc

bCalc

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scrnGC3: f(x) Plot Input

scrnGC4: g(x) Plot Input

The inputs above will be hidden when the program finally gets launched. Currently, I am not hiding them even when you close the calculator. The purpose of the inputs is to help in debugging. This allows you to enter simple code on the calculator screen but the program translates the input to javascript math. Give it a try and see if you notice any obvious problems or have suggestions for improvements.

gCalc

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Select precision* of answer:

Select angle mode:

Enter expression to evaluate here:

The answer is shown below:

Enter function to be plotted:

f(x) =

Enter 2nd function, if needed:

g(x) =

Change or reset the x-y scaling below:

x_min =

x_max =

y_min =

y_max =

Accuracy Disclaimer

The javascript math object methods used for this calculator are not accurate for very large or very small numbers. In particular, the trigonometric functions may yield very small answers that should actually be zero or very large answers that should be infinite. This typically occurs at 90° or pi/2 intervals.

DO NOT USE WHERE HIGH PRECISION IS REQUIRED. USE AT YOUR OWN RISK.

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The primary purpose of this lesson is to illustrate how to create a histogram. Histograms are used to graphically summarize statistical data. Sort the data (In this lesson, 50 random numbers, 0 to 79, are already sorted). Determine the range of the data (Largest number minus the smallest number). Decide how you would like to slice up your range of data, i.e. the class interval to use. Use at least 3 or 4 class intervals or bins of equal size, and no more than 10. Place each piece of data in the appropriate bin. Data falling on a boundry is promoted to the next bin. Count how many pieces of data ended up in each bin. This is the frequency. Create a vertical bar graph. No space should appear between the bars as the intervals should be continuous. The y-axis should show the frequency or number of occurences. The x-axis should show the complete range of the data. Experiment with different bin sizes to see dramatic differences in the graphical representation of the same data. The following data has been sorted, placed into two different size bins, counted and graphed for you.
50 Random Numbers (0 - 79 / sorted)

Data sorted by class interval, using 10 class intervals, or bins.
Class Interval	Data	Freq
0 - 8
8 - 16
16 - 24
24 - 32
32 - 40
40 - 48
48 - 56
56 - 64
64 - 72
72 - 80
Data sorted by class interval, using 8 class intervals, or bins.
Class Interval	Data	Freq
0 - 10
10 - 20
20 - 30
30 - 40
40 - 50
50 - 60
60 - 70
70 - 80
Graphing the bin and frequency data from above, yields the histograms shown below:



Summary: The 5-bin histogram can be derived from the 10-bin histogram since the larger class interval contains two smaller class intervals. The 4-bin histogram can be derived from the 8-bin histogram. A 2-bin histogram can be derived from the 4-bin histogram but should not be used. All other histograms can only be derived by analyzing the original data. Note: You can never get more definition from data that has already been grouped but you can always group data to reduce the number of bins.