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- 1. Statistics (P5)
- 2. Data that has not been organized into groups. Ungrouped data looks like a big list of numbers.
- 3. These statistics describe the “middle region” of the sample. Mean▪ The arithmetic average of the data set. Median▪ The “middle” of the data set. Mode▪ The value in the data set that occurs most frequently. These are almost never the same, unless you have a perfectly symmetricdistribution. Mode MedianMeanMode = Median = Mean
- 4. The Median is the middle observation of an ordered (fromlow to high) data set Examples: 1, 2, 4, 5, 5, 6, 8▪ Here, the middle observation is 5, so the median is 5 1, 3, 4, 4, 5, 7, 8, 8▪ Here, there is no “middle” observation so we take theaverage of the two observations at the center5.4254Median
- 5. The Mode is the value of the data set that occurs most frequently Example: 1, 2, 4, 5, 5, 6, 8▪ Here the Mode is 5, since 5 occurred twice and no other valueoccurred more than once Data sets can have more than one mode, while the mean andmedian have one unique value Data sets can also have NO mode, for example: 1, 3, 5, 6, 7, 8, 9▪ Here, no value occurs more frequently than any other,therefore no mode exists▪ You could also argue that this data set contains 7 modes sinceeach value occurs as frequently as every other
- 6. The mean, ( is calculated by taking the sumof the observed values (yi) divided by thenumber of observations (n).nyyynynnii211y
- 7. Determine the mean for the set: {2, 3, 7, 5, 5,13, 1, 7, 4, 8, 3, 4, 3} y1 = 2, y2 = 3, y3 = 7, y4 = 5, …, y13 = 3 n = 13 Mean =
- 8. The Mean, Median and Mode by themselves are notsufficient descriptors of a data set Example: Data Set 1: 48, 49, 50, 51, 52 Data Set 2: 5, 15, 50, 80, 100 Note that the Mean and Median for both data sets areidentical, but the data sets are glaringly different! The difference is in the dispersion of the data points Dispersion Statistics we will discuss are: Range Variance Standard Deviation
- 9. The Range is simply the difference between thesmallest and largest observation in a data set Example Data Set 1: 48, 49, 50, 51, 52 Data Set 2: 5, 15, 50, 80, 100 The Range of data set 1 is 52 - 48 = 4 The Range of data set 2 is 100 - 5 = 95 So, while both data sets have the same meanand median, the dispersion of the data, asdepicted by the range, is much smaller in dataset 1
- 10. It gives the amount of dispersion or scatter in the data fromthe central tendency (mean).Nyi2)(
- 11. Determine the standard deviation of the set:{5, 6, 8, 4, 10, 3} Mean = y = (y - )2 = (5 - )2 + (6 - )2 + (8 - )2 + (4 - )2 +(10 - )2 + (3 - )2 (y - )2 = 12 + 02 + 22 + (-2) 2 + 42 + (-3) 2 (y - )2 = 1 + 0 + 4 + 4 + 16 + 9 = 34 Standard deviation = σ = √( (y - )2 / n) σ = √ 34 / 6 = √ 5.666 = 2.380
- 12. TheVariance, σ 2, represents the amount of variability ofthe data relative to their meanNyi22)(
- 13. Determine the variance of the set of the set:{5, 6, 8, 4, 10, 3} As previously shown: Mean = (y - )2 = 34 n = 6 Variance = σ2 = (y - )2 / n = 34/6 = 5.666

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