# Statistics Study Guide

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Introduction

Statistics Study Guide Data are observations that have been collected (EX. Measurements, gender, survey responses) Statistics are a collection of methods for planning experiments, obtaining data, & then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusion based on the data. Stats are represented by a bell curve represents any population of anything. Census is the collection of data from every member of the population. Observational study- we observe and measure specific characteristics, but we don't attempt to modify the subjects being studied . Population is the complete collection of all elements to be studied. Parameter is a numerical measurement describing some characteristic of a sample. What is your data set composed of? Qualitative Data: Data are separated into different categories that are distinguished by same non-numerical characteristic. Quantitative Data - consist of numbers representing counts or measurements. Discrete data result when the number of possible values is either a finite number or a "countable" number (0, 1, 2, 3, etc.) Continuous (numerical) data results from infinitely many possible values that correspond to some continuous scale that covers a range of values without gaps, interruptions, or jumps. Ways to classify data Nominal data- characterized by data that consists of names labels, or categories. The data cannot be arranged in an ordering scheme (high to low, best to worst, Male or female) Ordinal- Can be arranged in same order, but difference between data values either cannot be determine or are meaningless. (1st, 2nd, 3rd....Likert scales: 1disagree...2...3...4...5...6 agree) Interval- distance between values becomes meaningful. However there is no natural zero starting point and ratios are meaningless. (none of the quantities are present) (Temperature 100-80=20... no mult or div) Ratio- Just like interval data, but add a natural zero staring point. For the values at this level, differences and ratios are both meaningful. (Can mult & div...no neg numbers) (Height, weight, prices, and distance traveled, miles per hr.) ...read more.

Middle

Variance- of a set of values is a measure of variation equal to the square of the standard deviation. Sample variance: Square of the standard deviation s. S= 7.0 min then, sample variance=s2=7.0 sq'd=49.0 min sq'd Population variance: Square of the population standard deviation. For estimating a value of the standard deviation s: to roughly estimate the standard deviation, use S=range/4 where range= (highest value)-(lowest value) Example.......... Lowest is 0 and highest is 491 so.......S= range/4 491/4=122.75=123 For interpting a known value of the standard deviation S: If the standard deviation s is known, use it to find rough estimates of the minimum and maximum "usual" sample values by using Min "usual" value= (mean) - 2 multiplied (standard deviation) Max "usual" value = (mean) + 2 multiplied (standard deviation) Example......the mean is 40.05cm and the standard deviation of 1.64cm Min= (mean) - 2 mult (standard deviation) 40.05 - 2(1.64) = 36.77 cm Max= (mean) + 2 mult (standard deviation) 40.05 + 2(1.64) = 43.33 cm A standard score, or z score, is the number of standard deviation that a given value x is above or below the mean. It is found using the following expressions: Sample Population Z= x- x/s Z= x - /o (round z to 2 decimal places) Percentile of a value x = number of values less than x/total number of value mult 100 L= (k/100)n where.....n= number of values......k= percentile in question Example......L= 68/100 multiplied by 40 = 27.2 then is it a whole # ? No ......change L by rounding it up to the next larger whole #...The Pk is the Lth value, counting from the lowest. Yes......The value of the Kth percentile is midway between the Lth value and the next value in the sorted set of data. Find Pk by adding the Lth value and the next value and diving the total by 2. Boxplot is a graph of a data set that constist of a line extending from the min value to the max value, and a box with lines drawn at the first quartile, q1; the median; and the third quartile, Q3. ...read more.

Conclusion

Complements: The probability of "at least one" is equivalent to "one or more" *The complement of getting at least one item of a particular type is that you get no items of that type. Conditional probability of an event is a probability obtained with the additional information that some other event has already occurred.P(B|A) denotes the conditional probability of event B occurring, given that event A has already occurred, and it can be found by dividing the probability of events A and B both occurring by the probability of the event A: P(B|A) = P(A and B)/P(A) Intuitive approach to conditional Probability The conditional probability of B given A can be found by assuming that event A has occurred and, working under that assumotion, calculating the proability that event B will occur. Simulation of a procedure is a process that behaves the same way as the ptocedure, so that similar results are produced. Fundamental Counting Rule For a sequence of two events in which the first event can occur m ways and the second event can occur n ways, the events together can occur a total of m X n ways. Notation The factorial symbol! Denotes the product of decreasing positive whole numbers. For example, 4! = 4 x 3 x 2 x 1 = 24. By special definition, 0! =1. ( Many calculators have a factorial key.) Factorial Rule A collection of n different items can be arranged in order n! different ways. (This factoral rule reflects the fact that the frist item may be selected n different ways, the second item may be selected n - 1 ways, and so on.) Permutations Rule (when items are all different) The number of permutations (for sequences) of r items selected from n available items (without replacement) is nPr = n!/(n -r)! Permutations Rule (when some items are identical to others) If there are n items with n1 alike, n2 alike,.....nk alike, the number of permutations of all n items is n!/ n1!n2!....nk! Combinations Rule The number of combinations of r items selected from n different items is nCr = n!/(n -r)!r! ...read more.

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