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MBF3C 3.6 Common Distributions Standard deviation should be looked at with respect to the mean. Let’s say the standard deviation for the prices of telescopes is $50. If the mean price is $200, then the standard deviation indicates a wide spread in the selling price. If the mean price was $1200, then the standard deviation indicates little variance in the selling price. One way to analyze data is to look at frequency, or the number of times, each value occurs. Ex: A driving test for a class of students had the following results out of 100, and whole marks were awarded. Mark 30-40 40-50 50-60 60-70 70-80 80-90 90-100 # of students 1 6 19 32 21 16 5 A bar graph showing the frequency of the marks: Driving Test Marks 35 30 25 20 15 10 5 0 30-40 40-50 50-60 60-70 70-80 80-90 90-100 We begin to see a distribution of data as a mountain peak arrangement. (approximated on graph through mid-points of each bar) If we were to sample enough data, we would start to see a smooth curve when the mark ranges were narrowed to a small difference (30-31, 31-32, etc) A symmetrical frequency distribution graph with the same mean, median and mode is called a normal distribution (bell-shaped) Note x is the symbol for mean and s (or )is the symbol for standard deviation. In a normal distribution, 68% of the numbers fall within 1 standard deviation of the mean, 95% are within 2 standard deviations of the mean and 99% are within 3. A bimodal distribution has two peaks, representing 2 modes and is also symmetrical about the centres. A skewed distribution is non-symmetrical. Skewed Bimodal Text Problems: 3.6 from Homework Checklist Pg 153 #1-7