BASIC STATISTICAL CONCEPTS

SECTION I. BASIC STATISTICAL CONCEPTS

1. Frequency distributions. Frequency distributions summarize data in relation to the different values in a data set. In effect, frequency distributions provide counts of the number of times that each value appears in a data set.

a. Mean. The mean is the average value of all of the values in a data set. The mean is obtained by adding together all the values in a data set and then dividing the total by the number of items in the data set.

b. Median. The median is the value in a data set that reflects the point at which equal numbers of all of the values will be either above or below the median value. The median may be one of the values in a data set; however, frequently the median will be a point between two values in a data set.

c. Mode. The mode is the value that appears most frequently in a data set. It is possible to have more than one mode in a data set.

a. Variance. Variance is a measure of dispersion around the mean. The variance is equal to the sum of squared deviations from the mean divided by one less than the number of cases.

b. Standard deviation. The standard deviation is an extension of the variance. The standard deviation is the square root of the variance. In a normal distribution, 68% percent of the cases will be within (+or-) one standard deviation of the mean, and 95% of the cases will be within (+or-) two standard deviation of the mean.

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24.86 Classical: Mean = 71.5; SD = 30.78 Rap: Mean = 51.9; SD = 22.07 Calculations: C&W 1 99 24.8 615.04 2 94 19.8 392.04 3 95 20.8 432.64 4 23 -51.2 2621.44 5 72 -2.2 4.84 6 81 6.8 46.24 7 79 4.8 23.04 8 28 -46.2 2134.44 9 94 19.8 392.04 10 77 2.8 7.84 Sum 742 6669.6 Mean 74.2 SD* 27.22 Variance 741.0667 * SD = Square Root: 741.0667 = 27.22 Rock 1 90 12.8 163.84 2 11 -66.2 4382.44 3 82 4.8 23.04 4 67 -10.2 104.04 5 95 17.8 316.84 6 93 15.8 249.64 7 73 -4.2 17.64 8 90 12.8 163.84 9 87 9.8 96.04 10 84 6.8 46.24 Sum 772 5563.6 Mean 77.2 SD* 24.86 Variance 618.1778 * SD = Square Root: 618.1778 = 24.86 Classical 1 52 -26.5 702.25 2 75 -3.5 12.25 3 91 12.5 156.25 4 94 15.5 240.25 5 97 18.5 342.25 6 39 -39.5 1560.25 7 83 4.5 20.25 8 85 6.5 42.25 9 100 21.5 462.25 10 69 -9.5 90.25 Sum 785 3628.5 Mean 78.5 SD* 20.08 Variance 403.1667 * SD = Square Root: 403.1667 = 20.08 Rap 1 74 22.1 488.41 2 32 -19.9 396.01 3 25 -26.9 723.61 4 45 -6.9 47.61 5 57

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