S1 Notes Essay

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S1 Notes Wednesday 27th May 2010 Mr Aroui Finding the Median, Lower Quartile and Upper Quartile using Interpolation: b is the lower class boundary, f is the sum of all the frequencies below b, [pic]is the frequency of the class, w is the class width. Median: [pic] Lower Quartile: [pic] Upper Quartile: [pic] Decile: [pic] Percentile: [pic] Finding the Mean, Variance and Standard Deviation: Mean: [pic] or [pic] Variance: [pic] or [pic] Standard Deviation: [pic] or [pic] Finding the Interquartile Range (IQR) and Semi-Interquartile Range (SIQR): [pic] [pic] Outliers: An outlier is any value, which is • Less than [pic] • Greater than [pic] Skewness: The shape(skewness) of a data set can be described using diagrams, measures of location and measures of spread.A distribution can be symmetrical, have positive skew or have negative skew. Using the Quartiles: [pic] then the distribution is symmetrical. [pic] > [pic] then the distribution is positively skewed. [pic] < [pic] then the distribution is negatively skewed.. Using the Measures of location (Mode, Median & Mean): [pic] describes a distribution which is symmetrical. [pic] < [pic]< [pic] describes a distribution which positive skew. [pic] > [pic]> [pic] describes a distribution which negative skew. [pic] this gives you a value and tells you how skewed the data is ❖ The closer to zero the more symmetrical ❖ A negative number means the data has negative skew. ❖ A positive number means the data has a positive skew Probability: P(A or B or both) = [pic] P(both A & B) = [pic] P(not A) = [pic] Addition Rule: [pic] Multiplication Rule: [pic] Conditional probability: [pic] Independent Events:If two events A and B are independent [pic] [pic] or [pic] Mutually Exclusive Events:If two events A and B cannot

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