![]() Quartiles are the 25th, 50th, and 75th percentiles.Statistics Tutorial Stat HOME Stat Introduction Stat Gathering Data Stat Describing Data Stat Making Conclusions Stat Prediction & Explanation Stat Populations & Samples Stat Parameters & Statistics Stat Study Types Stat Sample Types Stat Data Types Stat Measurement Levelsĭescriptive Statistics Stat Descriptive Statistics Stat Frequency Tables Stat Histograms Stat Bar Graphs Stat Pie Charts Stat Box Plots Stat Average Stat Mean Stat Median Stat Mode Stat Variation Stat Range Stat Quartiles and Percentiles Stat Interquartile Range Stat Standard Deviation If your data are not normally distributed, you might think about using the median and the interquartile range to report your data.ĭefinition of a percentile: a number, y, is in the nth percentile for the data if n% of the data are less than or equal to y. If you calculate a z-score and the conclusion is nonsensical (like a negative number of pizza slices eaten) this is a flag that your distribution is not normal Think about your distribution and whether or not it should a bell-shaped curveĮxamples: Number of pieces of pizza eaten by your friends at dinner? Most eat one or two, but there's always one way out there eating 6. If your data are not normally distributed, then using the normal distribution as an approximation will give you the wrong answer You can also use your percentile score on the SAT to estimate your IQ except for what? (Not everyone takes the SAT.) Then you put it in the equation (1.55 = (X - 100)/16) and find that your I.Q. First you look in the table to find out what z score cuts off 94% of the distribution, 1.55. So instead, she tells you that you are smarter than 94% of people. exactly because she thinks you'll end up with a swelled head. Let's say your teacher does not want you to know your I.Q. of 115 is smarter than about 83% of people, or 17% of people are smarter than Max.Įxample of translating percentile into a score ![]() We divide that in half and add 50% to get the correct %. From Table A we find that going out from that z-score on both sides cuts off 65.79 percent of people. units into z-units by using the equation. of 115, how much smarter is he than everybody else?įirst we translate the I.Q. scores have a normal distribution, approximately, with a mean of 100 and a standard deviation of 16. (Just like calendar days are a distribution where the scale is approximately the time it takes for earth to make one complete orbit around the sun)Īnd we can relate z directly to the normal distribution and so we know the percentile of the score What standard score cuts off 9.7% of the distribution to the left of score? (We know 100%-(2*9.7)%=80.6%, so we find z = 1.30, and we want the negative side so z = -1.30, or 1.3 standard deviations to the left)ĭefinition: z is a distribution that is scaled in standard units where the unit is standard deviations from the mean in a normal distribution. What percent of the standard normal curve lies below 1.75 standard deviations? (For 1.75 z, the area = 91.99%, 91.99/2 + 50 = 95.99%) The table in the book gives the area in percentages bounded on the positive and negative side by the z-value (which is equivalent in units like this: 1 z = 1 S.D.) Remember area under the curve is 100% 50% of the curve lies to either side of the mean The book gives many examples and lots of practice-good idea We know at any point on the x-axis what the density or area under the curve is Important properties of this line and the shape it createsĪrea under the curve is 100%-at 0 height is about 40%-draw two triangles and calculate area (1/2*40*± 3) as an approximation of the curve The result is what is called a bell-shaped curve You know the formula for a straight line: y = bx + c The normal curve is also a line but it is defined by: ![]() The normal distribution, also called the z-distribution ![]() Example: How frequently do you go to the student store on a 1 to 7 scale? How many days per week is that? Does knowing the standard units of days give us more information? Standard scales convey important information in addition to the value observed. We are now going to learn about a distribution (the z-distribution) that has some very handy attributes and we are going to learn how to translate our observations, scores, distributions, into that scale and back again We say URSA instead of the formal name (University Records System Access) to communicate We translate feet into inches to make addition easier, e.g. We already translate units all the time for convenience. This chapter is about taking advantage of something we know is true to give us an edge in making decisions-we do this by translation ![]()
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