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Statistic - The word statistics is...

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Unformatted text preview: The word statistics is d ' (meaning "state"). It method of analysis. can be used to refer to ote. It is virtually impdssible to obtain a consensus on the definition of.statistics, but it is possible to make a distinction between the following: A) Descriptive Statistics refers to t . . he collection, presentation, and summarization of data. B) Inferential Statistics isgthe area that attempts to make infarences (conclusions) about a pOpulation given data that were obtained from a sample drawn from the population. Definitions 1) A.Qopu1ation is a complete set of individuals, objects or measurements having some Common observable characteristic. 2) A freggencx distribution is a table that shows each score and the number of times that score occurs. - 3) The freggencx is the number of times a score appears. 4) The cumulative freggencx is the number of scores at and below a given point. . 5) Pregnancy golgons and histograms are graphical methods of displaying data. ; notes. i) A freggency polygon is similar to a line graph. ii) A histggram is similar to a bar'graph. 6) A measure of central tendgncy is an index of central location employed in the descriptiop of frequency distributions. Note. Statisticians have discovered that data often cluster around a ggpgggl=¥gégg that lies between the two extreme values. 7) An#brrax is an ordered arrangement of data. The following formula tells 333;; the median is located; it does HQT tell the value of the median. FORMULA: The ignition of the Median = number of scores + 1 2 8) A measure of dispersion measures the Spread or variability of data about the measure of central tendency. 9) SIGMA notation is used to facilitate the sum of many terms. It involves the symbol 2:, the capital sigma of the Greek alphabets, which corresponds to our letter S. In short, z:neans to “ADD". 3,3: 7.: r1 MeaSures of Central Tendency I. The ARITHMETIC MEAN is the fig; of the scores divided by the total number of scores. Example. Find the mean of 93, 85, 74, 92, 93, 86, and 107. + + + + + l I Mean: {93 85+“ 92 93 as 107 /? = 630/7 = E II. The MDDE is the score in a distribution that appears more than the other scores. Exggples. Find the mode(s) of the following distributions. a. l. l, 2. 2. 2. 3. 3, 3. 3. 4. 4, and 4 The mode is ; because it appears more than the other numbers, 4 times. b- 0. 1. 1; 2: 2. 2. 2. 2. 3. 3. 3. 3: 3. 4. 4. and 4 The modes are g=g§gm; because each score appears most often, 5 times. C. O, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, and 6 Since no score appears more than the others, this distribution has 39 Egg;- kbht m5, J: ‘7': (guflhz “”2" Sam} ~> 7}; us '.¥1‘%:rm\ 6M3 III- The MEDIAN is the score in the gggggg of a set of data that is arranged in either increasing g3 decreasing order. Remember. To find the median, the data MUfiI be arranged in an 3335! (either increasing or decreasing order}. Examples. Find the median of the following. a. 38, 32, 23, 27, 32, 31, 33, 26, and 29. Array: 23, 26, 2?, 29, 11, 32, 32, 33, 38 The score in the middle is 31. Thus, the median = 11. b- 23, 32, 3B, 27, 32, and 31. Array: 23, 27, £533, 32, 38 The middle score is between 31 and 32. Therefore, we must find the m of 31 and 32- Thus, [31 + 321/2 = 63/2 = median = EROBLE .5. For the following sample data, a) Set up a frequency distribution. b) Compute the arithmetic mean. c) Find the position of the median. d) Find the median. e) Find the mode. E) Find the range. 9) Compute the variance. h) Compute the standard deviation. i) Draw a histogram. j) Draw a frequency polygon. l) 1, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6 2) 1, l, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 8 :5! ...
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