4 sheets Midterm

# 4 sheets Midterm - Section 2.3 2.7 Center Spread...

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Section 2.3- 2.7 Center Spread Calculating median, m Arrange the n measurements from smallest to largest 1. If n is odd m is the middle number 2. If n is even m is the mean of the middle two numbers Skewed data- Median <Mean- Rightward skewness Mean=Median symmetric Median Mean Mean Median Mean<Median- Leftward skewness (Rightward) (Leftward) Mode- Most frequently Range- Largest measurement minus the smallest measurement Sample variance- or Sample standard deviation- Standard deviation: The amount of variability in the [time] it takes something to complete Chebyshevs Rule: Interpreting the standard deviation. Applies to any data set regardless of the shape of the frequency distribution of the data No useful information is provided on the fraction of measurements that fall within 1 standard deviation At least ¾ will fall with 2 standard deviations of the mean At least 8 / 9 will fall with 3 standard deviations of the mean Generally, for any number k greater than 1, at least (1-1/k 2 ) of the measurements will fall within k standard deviation of the mean Empirical Rule: Applies only to symmetrical (Normal) bell/mound shaped distributions Approximate but more precise than Chebyshavs theorem It apples to population of sample data Interval Contains Approximately 68% of measurements Approximately 95% of measurements Approximately 99.7% of measurements (Almost all) p th percentile- p% fall below and (100-p)% fall above z-score- Distance between a given measurement x and the mean, expressed in standard deviations Approximately 68% of measurements- Between -1 and 1 (-1,1) Approximately 95% of measurements- Between -2 and 2 (-2,2) Approximately 99.7% of measurements- Between -3 and 3 (-3,3) Section 3.1-3.6 Probability Rules for Sample Points (Sample Points- The most basic outcome of an experiment): Let p i represent the probability of sample point i 1. All sample point probabilities must lie between 0 and 1

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4 sheets Midterm - Section 2.3 2.7 Center Spread...

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