STAT200 Exam 1 Study Guide

# STAT200 Exam 1 Study Guide - Lessons 1+2 After looking at...

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Lessons 1+2 After looking at this lesson, you should know: the importance of graphing your data how to interpret the shape of a distribution what is a five-number summary and its interpretation the meaning of descriptive statistics what "average" means in statistics-speak the relationship between mean and median of a distribution some basic Minitab statistics and graphing methods Four features to consider for quantitative variables are: 1. Shape 2. Location (center or average) 3. Spread (variability) 4. Outliers Shape The shape of a dataset is usually described as either symmetric , meaning that it is similar on both sides of the center, or skewed , meaning that the values are more spread out on one side of the center than on the other. If it is skewed to the right (or positivey skewed) , the higher values (toward the right on a number line) are more spread out than the lower values. If it is skewed to the left (or negatively skewed) , the lower values (toward the left on a number line) are more spread out than the higher values. A symmetric dataset may be bell-shaped or another symmetric shape. The shape is called unimodal if there is one prominent peak in the distribution, and is called bimodal if there are two prominent peaks. Symmetrical: Data skewed to the right Mean = 6.94h, Median = 7h Mean = 14.3h, Median = 10h Bimodal Shape Location The word location is used as a synonym for the “middle” or “center” of a dataset. There are two common ways to describe this feature. 1. The mean is the usual numerical average, calculated as the sum of the data values divided by the number of values. It is nearly universal to represent the mean of a sample with the symbol , read as “x-bar.” 2. The median of a sample is the middle data value for an odd number of observations, after the sample has been ordered from smallest to largest. It is the average of the middle two values, in an ordered sample, for an even number of observations. Spread (also known as Variability) e Range = Largest – Smallest. This is the distance across 100% of the data. It will be highly sensitive to outliers. f Interquartile Range = IQR = Q3 – Q1. This is the distance across the middle 50% of the data. f Standard deviation = roughly, the average difference between individual data and the mean. This is the most common measure of variation. Example of Standard Deviation: Five students are asked how many times they talked on the phone yesterday. Responses are 4, 10, 1, 12, 3 . Step 1 : Calculate the sample mean. = (4+10+1+12+3)/ 5 = 30/5 = 6. Step 2 : For each value, find the difference between it and the mean. Data Value Deviation from mean 4 -2 (4 – 6) 10 4 (10 - 6) 1 -5 (1- 6) 12 6 (12- 6) 3 -3 (3 - 6) Step 3 : Square each deviation found in step 2 Data Value Deviation from mean Squared Deviation 4 -2 4 10 4 16 1 -5 25 12 6 36 3 -3 9 Step 4 : Add the squared deviations found in step 3 and divide by (n – 1) (4 + 16 + 25 + 36 + 9 ) / (5 – 1) = 90 / 4 = 22.5.

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## STAT200 Exam 1 Study Guide - Lessons 1+2 After looking at...

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