# Bars show frequency of scores in each 5 range more

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Bars show frequency of scores in each 5% range More close together / higher grades = best class More spread apart = more variety in scores Constructing a Frequency Distribution Using Grouped Qualitative Data What it means Numbers that aren’t whole numbers à need to group these number sets into classes to limit results Number of Classes 2 k > n rule - k = number of classes - n = number of data points Find lowest value of k that satisfies that rule Ex: 50 data points - 2 k > 50 - 2^5 = 32 > 50 (too small) - 2^6 = 64 > 50 (perfect) Class Width Determining Class Width Width = breadth (range) of numbers we plan to put into each class Estimated class width = (max data value – min data value) ¸ k Example: where k equals 6, max data value equals 17.4, and min data value equals 0.6 (17.4 – 0.6) ¸ (6) = 2.8 Other Rules
Round to whole number No correct answer (can round 2.8 up to 3 or 4) - b/c trying to identify useful pattern in the data, and there’s often more than one way to do this Class Boundaries Class Boundaries – the minimum and maximum values for each class Choosing Class Boundaries Try to stick with whole numbers Stick to your class width Ex: min data value equals 0.6 and class width is 3, and number of classes equals 6 0 to less than 3 3 to less than 6 6 to less than 9 9 to less than 12 12 to less than 15 15 to less than 18 Ex: min data value of 0.6, class width of 4, and number of classes of 6 - Allows 6 classes, but okay if less than 6 classes - Below = if we’d chosen class width of 4, rather than 3 0 to less than 4 4 to less than 8 8 to less than 12 12 to less than 16 16 to less than 20 Class Frequencies How to find it Count number of observations in each class and record the total Rules: Constructing Classes for Grouped Data Equal-Size Classes - all classes in the frequency distribution must be equal width Mutually Exclusive Classes - The class boundaries cannot overlap, b/c specific data points can end up in more than one class - Ex: 0 to less than 3 / 2.5 to less than 5.5 (NO) Include All Data Values Avoid Empty Classes - Don’t display classes so narrow that there are no observations in it
Avoid Open-Ended Classes (if possible) - Example of open-ended class: 18 and over (rather than 18 to less than 21) Constructing a Histogram with Grouped Quantitative Data Steps for Creating Histogram Use continuous data listed in table 2.6 (page 30) Same steps as listed before for Excel (data used listed below) Edits for Histogram of Continuous Grouped Data Format the data series and drag the “gap width” to the left Format Axis > Alignment > Custom Angle (-45) The Consequences of Too Few or Too Many Classes To Few Classes Happens if use to wide of classes à obscures patterns Shows to little data (ex: if class width of 9, may only have two classes) à only two bars in your histogram To Many Classes Happens if too narrow of classes
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