How to Use the Histogram Applet

  1. The IQ data for the McGlone problem (Assignment 3, #3) appears in the text field to the right of the applet.  To determine the class interval width and the number of intervals, your first task would be to sort the data.  This is easily accomplished by clicking on the sort button located on the menu line at the bottom of the applet.

  2. Once the data is sorted, compute the range [(highest - lowest) +1].  Rule of thumb #1 is that your grouped frequency distribution should contain about 10 intervals, so to determine the interval width, take the range and divide by 10.  You should have computed the range to be 47 - [(125-79) + 1].

  3. Divide the range by 10 - the result is 4.7.  Logical choices for the interval width, then, are 4 and 5.  Since 5 is an odd number and is easily interpretable with this type of data, it is a good choice for the interval width.

  4. The next job is to determine where to begin the first interval.  This is a straightforward task.  Start with the lowest score in the distribution.  Is it divisible by the interval width?  If the answer is yes, then start your first interval at that number.  If the answer is no, then find the first number that is less than the minimum score and divisible by the interval width.  In this case, 79 is not divisible by 5, so we back up the interval start point to 75 and the first interval becomes 75 to 79.

  5. To display a histogram for this data, go to the Choose Mode button on the applet menu line.  Select histogram.  The default number of intervals is set at 10, but you can change the intervals by clicking the increase or decrease buttons on the menu line next to the interval window.

  6. If the first interval is set at 75 to 79, then the midpoint of the interval will be 77 and the lower exact limit of the interval will be 74.5.  In the default display, the interval width is equal to 5, but the midpoint is 79.  How do you know the interval width from looking at the histogram?  You can tell by looking at the interval midpoints.  The distance between the midpoints is equal to interval width. : In the applet, the midpoints are displayed for every other interval so the distance is determined by taking the computed midpoint distance and dividing it by 2 to get 5.

  7. If you increase the number of intervals to 11, the interval width will remain at 5 but the midpoints are readjusted so that the first interval begins at 75 and extends to 79.