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MAT 110 Vocabulary Ch 14 14.1 STATISTICS: an area of mathematics in which we gather, organize, analyze and make predictions from numerical information called DATA or a DISTRIBUTION SAMPLE: a subset of a population BIASED: does not accurately reflect the population as a whole – 2 types: SELECTION and LEADINGQUESTION BIAS FREQUENCY DISTIBUTION: a set of data listed with their frequencies RELATIVE FREQUENCY DISTRIBTION: showing the percent of time that each item occurs in a frequency distribution (usually expressed as a decimal) REPRESENTATION OF DATA: See pages 703-710 for specific examples: FREQUENCY TABLE, BAR GRAPH, HISTOGRAM, and STEM AND LEAF DISPLAY 14.2 MEASURES OF CENTRAL TENDENCY: mean, median, mode and quartiles MEAN: average of the data (notation 𝑥̅ or µ) MEDIAN: the middle number in a list of data when arranged in order. If there are two middle numbers, then they must be averaged MODE: the number that appears most frequently. (There can be two modes if two numbers appear the most or no mode if more than two scores appear most frequently.) FIVE-NUMBER SUMMARY: Lowest value, Q1 (Median of the lower half), MEDIAN, Q3 (Median of the upper half), Highest value BOX AND WHISKER PLOT: a graph that represents the five-number summary: Q1 Q2 Q3 source: ellerbruch.nmu.edu 14.3 RANGE: the difference between the largest and smallest data values (Largest # minus smallest #) DEVIATION FROM THE MEAN: distance a number is form the mean (negative if below the mean, positive if above) ( x - 𝑥̅ ) MAT 110 Vocabulary Ch 14 STANDARD DEVIATION : a measure based on the distance each data value is from the mean (s or σ) ∑(𝑥− 𝑥̅ )2 𝑠= √ Formula: 1. 2. 3. 4. 5. 𝑛−1 which is to: Find the mean for the data Find the deviation from the mean for each Square the values in 2. Add up the squares and then divide by n – 1 (the value at this point is called VARIANCE) Calculate the square root of the answer to step 4 𝑠 COEFFICIENT OF VARIATION: CV = 𝑥̅ ∙ 100 % 14.4 NORMAL CURVE or NORMAL DISTRIBUTION: the most common distribution and describes many reallife data sets; Bell-shaped curve; mean median and mode the same; symmetric with respect to the mean; area under the curve equals 1 34% 2.5% 13.5% 34% 13.5% 2.5% Source: www.syque.com Roughly 68% of data is with 1 standard deviation from the mean, 95% are within 2 standard deviations from the mean and 99.7% are within 3 standard deviations of the mean. Z – SCORE: the number of standard deviations a data value is from the mean. If a normal distribution has a mean of µ and a standard deviation of σ then you can convert a 𝑥− 𝜇 data value, x, to a z-score with the formula: 𝑧 = 𝜎