ANATOMY OF SUMMARY STATISTICS Measures of Central Tendency

ANATOMY OF SUMMARY STATISTICS: Measures of Central Tendency, Variation and Position 440 481 482 483 514 554 554 562 612 623 631 638 664 671 677 690 707 The Minimum is the smallest value in a data set. Mean: The mean of a data set, is the sum of all values in the data set, divided by the number of values in the data set. Here, the sum of all data values is 11534, and there are 20 data values, therefore the mean is 11534/20 = 576. 7 lbs. The Mode is the most frequently occurring value in a data set. Here the mode is 554 lbs. Note that it is possible to have more than one mode in a data set. * Standard Deviation: The standard deviation is used in conjunction with the mean. It represents a measure of distance from a given value to the mean. Median: The median is the value in the middle position, in a data set that has been ordered from smallest to largest. Here, the middle position is between two values, therefore, we add the two values, and divide their sum by 2. In this case, the median is (554 + 562)/2 = 558 lbs. Inter-Quartile Range: A measure of the middle 50% of a distribution’s data. It is often used in conjunction with the median as a measure of dispersion. Range: The range of a data set is the difference between the The Maximum is the largest value in a data set. *A data set containing two modes is called bimodal. A data set containing more than two modes is called multi-modal. The Data: The data set comes from Dudley’s Doughnuts. It is the amount of flour (in pounds) used on each of 20 consecutive days in December 1999. The data have been ordered from smallest to largest in value. maximum value, and the minimum value. Here, the range is 707 - 440 = 267 lbs. Midrange: The midrange of a data set is the difference between the maximum value and the minimum value, divided by 2. Here the midrange is (707 - 440)/2 = 133. 5 lbs.