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General Divisions Descriptive Statistics –Goal is to summarize or describe the data Inferential Statistics –Using data from a sample to make inferences (generalizations) about the population

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Major Descriptors Center: Where the “middle” of the data is Variation: How spread out the data is Distribution: The shape of the distribution of the data (if the data follows a pattern) Outliers: Data that is unusually separated from rest of data Time: How data changes over time

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Frequency Distribution A frequency distribution lists data values (or groups of data values) along with how many data had that value (the frequency, or count)

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Some data: Quiz scores 1213 1415 16 17 18 19 20

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Quiz scores: Frequency Distribution 1213 1415 16 17 18 19 20 ScoreFrequency 121 132 141 152 163 175 185 194 202

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Quiz scores: Frequency Distribution Using Classes 1213 1415 16 17 18 19 20 ScoreFrequency 12-144 15-1710 18-2011

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Definitions Lower class limits –Smallest numbers that can belong to a class Upper class limits –Largest numbers that can belong to a class Class boundaries –Numbers used to separate classes so that there are no gaps –For our purposes, we will just use lower class limits Class midpoint –Add upper and lower limits and divide by 2 Class width –The difference between consecutive lower class limits

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Example Lower class limits 12, 15, 17 Upper class limits 14, 17, 20 Class midpoints 13, 16, 19 Class width 3 ScoreFrequency 12-144 15-1710 18-2011

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Constructing a Frequency Distribution Choose number of classes you want –Usually 5 to 20, based on data and convenience Calculate class width –(highest value – lowest)/number classes –Usually round (up) –Sometimes handy to work backwards Choose starting point –Usually lowest value, or a little smaller

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Constructing a Frequency Distribution Use starting point and class width to list other lower class limits –Add class width to previous lower limit Add upper class limits Tally data into frequency table

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Example: Hours slept by caffeine drinkers Data: 1.2, 2.9, 3.1, 3.5, 4.1, 4.6, 4.8, 5.0, 5.3, 5.3, 5.4, 5.7, 6.3, 6.7, 6.7, 6.8, 6.9, 7.0, 7.1, 7.2, 7.2, 7.4, 7.5, 7.5, 7.8, 8.1, 8.2, 8.2, 8.5, 8.6, 9.3, 10.1 Choose number of classes: 5 (?) Class width: (10.1 – 1.2)/5 = 1.78 Lets round up to 2 and use that

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Example: Hours slept by caffeine drinkers Data: 1.2, 2.9, 3.1, 3.5, 4.1, 4.6, 4.8, 5.0, 5.3, 5.3, 5.4, 5.7, 6.3, 6.7, 6.7, 6.8, 6.9, 7.0, 7.1, 7.2, 7.2, 7.4, 7.5, 7.5, 7.8, 8.1, 8.2, 8.2, 8.5, 8.6, 9.3, 10.1 Starting point: Probably 1.0 (could start at 0.0)

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Example: Hours slept by caffeine drinkers Data: 1.2, 2.9, 3.1, 3.5, 4.1, 4.6, 4.8, 5.0, 5.3, 5.3, 5.4, 5.7, 6.3, 6.7, 6.7, 6.8, 6.9, 7.0, 7.1, 7.2, 7.2, 7.4, 7.5, 7.5, 7.8, 8.1, 8.2, 8.2, 8.5, 8.6, 9.3, 10.1 List lower class limits Lower Class limits 1 3 5 7 9

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Example: Hours slept by caffeine drinkers Data: 1.2, 2.9, 3.1, 3.5, 4.1, 4.6, 4.8, 5.0, 5.3, 5.3, 5.4, 5.7, 6.3, 6.7, 6.7, 6.8, 6.9, 7.0, 7.1, 7.2, 7.2, 7.4, 7.5, 7.5, 7.8, 8.1, 8.2, 8.2, 8.5, 8.6, 9.3, 10.1 Add upper class limits Hours slept 1 – 2.9 3 – 4.9 5 – 6.9 7 – 8.9 9 – 10.9

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Example: Hours slept by caffeine drinkers Data: 1.2, 2.9, 3.1, 3.5, 4.1, 4.6, 4.8, 5.0, 5.3, 5.3, 5.4, 5.7, 6.3, 6.7, 6.7, 6.8, 6.9, 7.0, 7.1, 7.2, 7.2, 7.4, 7.5, 7.5, 7.8, 8.1, 8.2, 8.2, 8.5, 8.6, 9.3, 10.1 Tally data Hours sleptFrequency 1 – 2.92 3 – 4.95 5 – 6.910 7 – 8.913 9 – 10.92

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Relative Frequency Relative frequency = class frequency / sum of all frequencies Relative frequencies are expressed as percents

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Example: Hours slept by caffeine drinkers Hours sleptFrequencyRelative Frequency 1 – 2.922/32 = 6% 3 – 4.955/32 = 16% 5 – 6.91010/32 = 31% 7 – 8.91313/32 = 41% 9 – 10.922/32 = 6% Sum of Frequencies: 32 = sample size

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Cumulative Frequency Distribution Class limits are replaced with “less than” statements Frequency is frequency of data less than the class

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Example: Hours slept by caffeine drinkers Hours sleptCumulative Frequency Less than 32 Less than 57 Less than 717 Less than 930 Less than 1132 Hours sleptFrequency 1 – 2.92 3 – 4.95 5 – 6.910 7 – 8.913 9 – 10.92

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Homework 2-2: 1, 5, 9, 15 The answer the books gives for class boundaries will be different than what we’ve discussed in class.

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