how to quantify the center and spread of a distribution with various numerical measures;<\/p>\r\n<\/li>\r\n \t
some of the properties of those numerical measures; and<\/p>\r\n<\/li>\r\n \t
how to choose the appropriate numerical measures of center and spread to supplement the histogram.<\/p>\r\n<\/li>\r\n<\/ul>\r\n
Measures of Center<\/h2>\r\n\r\n\r\nIntuitively speaking, the numerical measure of center is telling us what is a \u201ctypical value\u201d of the distribution.\r\n\r\n<\/div>\r\nThe three main numerical measures for the center of a distribution are the\u00a0mode<\/em>, the\u00a0mean<\/em>\u00a0and the\u00a0median<\/em>. Each one of these measures is based on a completely different idea of describing the center of a distribution. We will first present each one of the measures, and then compare their properties.<\/p>\r\n\r\n\r\n\r\nMode<\/span><\/h2>\r\nSo far, when we looked at the shape of the distribution, we identified the mode as the value where the distribution has a \u201cpeak\u201d and saw examples when distributions have one mode (unimodal distributions) or two modes (bimodal distributions). In other words, so far we identified the mode visually from the histogram.<\/p>\r\n
Technically, the mode is the most commonly occurring value in a distribution. For simple datasets where the frequency of each value is available or easily determined, the value that occurs with the highest frequency is the mode.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n
\r\n\r\n\r\nExample<\/h3>\r\n<\/header>\r\n\r\nBest Actress Oscar Winners<\/h4>\r\n\r\nWe will continue with the Best Actress Oscar winners example. (To see the full dataset, Dataset_ Best Actress Oscar Winners (1970\u20132013)<\/a><\/p>\r\nTo find the most commonly occurring, or\u00a0modal<\/em>, age, it is helpful to list the ages in a frequency table, which gives the following results:<\/p>\r\n\r\n
The three main numerical measures for the center of a distribution are the\u00a0mode<\/em>, the\u00a0mean<\/em>\u00a0and the\u00a0median<\/em>. Each one of these measures is based on a completely different idea of describing the center of a distribution. We will first present each one of the measures, and then compare their properties.<\/p>\r\n\r\n So far, when we looked at the shape of the distribution, we identified the mode as the value where the distribution has a \u201cpeak\u201d and saw examples when distributions have one mode (unimodal distributions) or two modes (bimodal distributions). In other words, so far we identified the mode visually from the histogram.<\/p>\r\n Technically, the mode is the most commonly occurring value in a distribution. For simple datasets where the frequency of each value is available or easily determined, the value that occurs with the highest frequency is the mode.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n We will continue with the Best Actress Oscar winners example. (To see the full dataset, Dataset_ Best Actress Oscar Winners (1970\u20132013)<\/a><\/p>\r\n To find the most commonly occurring, or\u00a0modal<\/em>, age, it is helpful to list the ages in a frequency table, which gives the following results:<\/p>\r\n\r\nMode<\/span><\/h2>\r\n
Example<\/h3>\r\n<\/header>\r\n
Best Actress Oscar Winners<\/h4>\r\n
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