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  Ani, Cedric James D.   BSEE-2104 18-50158   ENGINEERING DATA ANALYSIS   MEASURES OF LOCATION Measures of location summarize a list of numbers by a typical value. The three most common measures of location are the mean, the median, and the mode. The mean is the sum of the values, divided by the number of values. It has the smallest possible sum of squared differences from members of the list. The median is the middle value in the sorted list. It is the smallest number that is at least as big as at least half the values in the list. It has the smallest possible sum of absolute differences from members of the list. The mode is the most frequent value in the list (or one of the most frequent values, if there are more than one). It differs from the fewest possible members of the list.  1.) QUARTILE    A quartile is a type of  quantile. The first quartile ( Q 1 ) is defined as the middle number between the smallest number and the median of the data set. The second quartile ( Q 2 ) is the median of the data. The third quartile ( Q 3 ) is the middle value between the median and the highest value of the data set. 9i60l2.2301j0j4&sourceid=chrome&ie=UTF-8   2.) DECILE  A decile is a quantitative method of splitting up a set of ranked data into 10 equally large subsections. A decile rank arranges the data in order from lowest to highest and is done on a scale of one to ten where each successive number corresponds to an increase of 10 percentage points. Deciles sort data into ten equal parts: The 10th, 20th, 30th, 40th, 50th, 60th, 70th, 80th, 90th and 100th percentiles. For example, if you were in the 99th percentile for a particular test, that would put you in the decile ranking of 10. 3.) PERCENTILE   In statistics, percentiles are used to understand and interpret data. The n th percentile of a set of data is the value at which n  percent of the data is below it. In everyday life, percentiles are used to understand values such as test scores, health indicators, and other measurements. For example, an 18-year-old male who is six and a half feet tall is in the 99th percentile for his height. This means that of all the 18-year-old males, 99 percent have a height that is equal to or less than six and a half feet. An 18-year-old male who is only five and a half feet tall, on the other hand, is in the 16th percentile for his height, meaning only 16 percent of males his age are the same height or shorter.      MEASURE OF VARIABILITY  Statisticians use summary measures to describe the amount of variability or spread in a set of data. The most common measures of variability are the range, the interquartile range (IQR), variance, and standard deviation. There are four frequently used measures of variability: the range, interquartile range, variance, and standard deviation.   RANGE  Range is defined as a single number representing the spread of the data. The range is the simplest measure of variability to calculate, and one you have probably encountered many times in your life. The range is simply the highest score minus the lowest score. variabi lity-range-variance-standard-deviation.html MEAN ABSOLUTE VALUE   The mean absolute deviation of a dataset is the average distance between each data point and the mean. It gives us an idea about the variability in a dataset. The equation |x|=a has two solutions x = a and x = -a because both numbers are at the distance a from 0. BOX AND WHISKER PLOT   In a box and whisker plot: the ends of the box are the upper and lower quartiles, so the box spans the interquartile range. the median is marked by a vertical line inside the box. the whiskers are the two lines outside the box that extend to the highest and lowest observations.   FUNDAMENTAL PRINCIPLES OF COUNTING The Fundamental Counting Principle (also called the counting rule) is a way to figure out the number of outcomes in a probability problem. Basically, you multiply the events together to get the total number of outcomes.    FACTORIAL NOTATION For example, for any number 'n', we can make n×(n-1)×(n-2)×(n-3)×(n-4)×(n- 5)×…×3×2×1. This is where we use the factorial notation. We define the factorial of a positive integer as the product of the integer with all the numbers lesser than it all the way up to 1.   PERMUTATION    A permutation is an arrangement of all or part of a set of objects, with  regard to the order of the arrangement. Formula: nPr = n(n - 1)(n - 2) ... (n - r + 1) = n! / (n - r)! Examples: In a set of (0,1,2,3,4,5,6,7,8,9) there are 10 numbers to choose from, but we will choose just 3 of them. 10 x 10 x 10 (3 times) = 10 3  = 1,000 permutations In a billiard game, there are 10 balls. Now we will choose 3 of them that can be in. So, for example we choice 1,2,3 and get their permutations. 10 x 9 x 8 = 720 permutations There are 720 different ways that 3 pool balls could be in out of 10 balls. COMBINATION  A combination is a selection of all or part of a set of objects, without regard to the order in which objects are selected. Formula: n C r   = n(n - 1)(n - 2) ... (n - r + 1)/r! = n! / r!(n - r)! = n P r   / r! Examples: In given data; 1,2,3,4 . Let’s find out how many ways 1,2,3 ,4 can be placed in order with the use of combination. 4! = 4 x 3 x 2 x 1 = 24 combinations It means that there are 6 ways you can put 1,2,3,4 in order. There are five anime: Diamond No Ace, Pokemon, One-Punch Man, Slamdunk, and Naruto and cream. Let’s fin d out how many ways of watching 3 anime from those five anime. There are 35 ways of watching 3 anime from five anime.
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