MAT243 - 2.5 Histograms.doc - 2.5 Histograms Histograms with evenly-sized bins A frequency distribution is a table that displays how often an outcome

# MAT243 - 2.5 Histograms.doc - 2.5 Histograms Histograms...

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2.5 Histograms Histograms with evenly-sized bins A frequency distribution is a table that displays how often an outcome occurs for a sample. To construct a frequency distribution, the data set is divided into mutually exclusive classes . A class is either a value of a categorical variable or an interval of a continuous variable. The frequency of a class is the number of events or values that fall under each class. Ex: An informal poll among a group of friends tallies how many people have x gaming applications on their phone. The results of the poll can be summarized in the frequency distribution below. Table 2.5.1: Frequency distribution showing the number of people in a group having x gaming apps on their phone. Gaming apps (x) Tally Frequency 0 |||| 4 1 |||| || 7 2 |||| 5 3 ||| 3 4 || 2 Feedback? The most common graphical representation of a frequency distribution is a histogram. A histogram depicts data values by splitting a continuous variable into a number of class intervals, each known as a bin. The simplest and most common type of histogram has bins of equal size. When bin sizes are equal, bins have rectangular bars with heights representing the frequency, which is the number of values in a bin. The x -axis contains a continuous number line with ticks that represent bin boundaries. A bin includes values equal to or greater than the lower boundary, but less than the upper boundary (lower value < upper). Gaps between rectangles are removed to show that the data is continuous. PARTICIPATION ACTIVITY 2.5.1: Histogram of number of tickets per miles per hour over speed limit. 1234

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2x speed 24 16 17 12 10 14 19 4 13 18 9 11 9 24 28 24 14 16 12 10 19 4 24 18 11 13 9 9 28 0 5 10 15 20 25 30 MPH over speed limit for 15 tickets issued: 2 4 6 Frequency (number of tickets) MPH over speed limit 17 1 3 5 Each bin frequency is represented by a rectangular column. Feedback? PARTICIPATION ACTIVITY 2.5.2: Histogram fundamentals.
Consider the following histogram showing speeding tickets issued by Officer Brown: 1) 3 speeding tickets were issued between 5−10 mph. True False Correct The rectangle for the 5−10 mph bin has a height of 3. 2) The most speeding tickets were given in the 15−20 mph range. True False Correct The rectangle for the 15−20 mph, at height 5, is taller than any other bin's rectangle. 3) The number of speeding tickets issued between 0−5 mph is unknown. True False Correct An empty bin indicates the frequency is (known to be) 0, so no tickets were issued between 0−5 mph. 4) A ticket issued that is 5 mph over the speed limit should be placed in the 0−5 mph bin.

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True False Correct A 5 mph ticket should be placed in the 5−10 mph bin because a number on the upper boundary of a bin's range (ex: 0−5 mph bin) should be placed in the next bin.
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