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STATS 2B03 (25)
Chapter 2

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Aaron Childs

STATS 2B03: Statistical Methods for Science Chapter 2: Descriptive Statistics 2.3 Grouped Data: The Frequency Distribution - main purpose in grouping data is summarization, making it easier to determine the nature of the information - class intervals: set of contiguous, nonoverlapping intervals such that each value in the set of observations can be placed in only one interval. There should be no fewer than 5 intervals and no more than 15 - Sturges’s rule: k = 1 +3.322(log n109, where k stands for the number of class intervals and n is the number of values in the data set - Class interval width: w = R/k, where R is the difference between the smallest and the largest observation in the data set - Frequency distribution: shows the way in which the values of the variable are distributed among the specified class intervals - Relative frequency of occurrence: proportion of values falling within a class interval - Relative frequencies: proportion of values falling within a particular class interval - Cumulate: sum the frequency or relative frequency of values within two or more contiguous class intervals - Histogram: display frequency distribution graphically referring to the space enclosed by the boundaries of the histogram as the area of the histogram - Frequency polygon: frequency distribution portrayed graphically, line graph. The total area under the frequency polygon is equal to the area under the histogram - Stem-and-leaf displays: provides information regarding the range of the data set, shows the location of the highest concentration of measurements, and reveals the presence or absence of symmetry. 2.4 Descriptive Statistics: Measures of Central Tendency - descriptive measure: summarization of data by means of a single number - statistic: descriptive measure computed from the data of a sample - parameter: descriptive measure computed from the data of a population - arithmetic mean: average obtained by adding all the values in a population or sample and dividing by the number of values that are added  general formula for the mean: ∑  sample mean: ∑  properties of the mean: 1. uniqueness 2. simplicity 3. affected by each value - median: value which divides the set into two equal parts such that the number of values equal to or greater than the median is equal to the number of values equal to or less than the median: (n+1)/2th  properties of the median: 1. uniqueness 2. simplicity 3. not as drastically affected by extreme values - mode: value which occurs most frequently and can be used for describing qualitative data - bell-shaped curve: when the mean, median and mode are equal, normal distribution also observed in t-distribution - skewness: whether data is symmetric or asymmetric. If the graph (histogram or frequency polygon) of a distribution is asymmetric, the distribution is said to be skewed. If a distribution is not symmetric because its graph extends further to the right than to the left we say the distribution is skewed to the right (positively skewed). If a distribution is not symmetric because its graph extends further to the left than to the ri
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