Chapter 3 Review MDM 4U Mr. Lieff

3.1 Graphical Displays be able to effectively use a histogram name and be able to interpret the various types of distributions ex: when would we use a histogram vs. a bar graph? ex: how do you calculate bin width? (range) ÷ (# of bars)

3.2 Central Tendency Be able to calculate mean, median, mode and weighted mean ex: determine which measure is appropriate Be aware of the effect of outliers Affect the mean more than the median Recognize the location of the measures with respect to skewed distributions if mode < median < mean…right skew If mean < median < mode…left skew

3.3 Measures of Spread Be able to calculate and interpret range, IQR and (population) standard deviation Up to 6 data points for std.dev. A larger value for ANY measure of spread (range, IQR, std.dev.) means the data has more spread IQR gives the range containing the middle 50% of the data IQR = Q3 – Q1

3.3 Measures of Spread cont’d How to calculate IQR Order the data!!! Find the median, Q2 Find the 1 st half median, Q1 Find the 2 nd half median, Q3 IQR = Q3 – Q1 Std.dev. Find the mean Find the deviations (data – mean) Square deviations Avg deviations Take square root

3.4 Normal Distribution Be familiar with the characteristics of a Normal Distribution (68–95–99.7% rule) Calculate the ranges of expected data based on 1, 2 or 3 std.dev. above and/or below the mean Ex: If a set of data has mean 10 and standard deviation 2, what percent of the data lie between 6 and 14? ans: 6 is 2 std dev below the mean and 14 is 2 std dev above. So 95% of the data falls in the range (see diagram)

Normal Distribution 34% 13.5% 2.35% 68% 95% 99.7% xx + 1σx + 2σx + 3σx - 1σx - 2σx - 3σ 0.15%

Normal Distribution Ex: If a set of data has mean 10 and standard deviation 2, what percent of the data lie between 8 and 14? Ans: 34% + 34% % = 81.5%

3.5 Z-Scores Standard normal distribution 1) Be able to calculate a z-score 2) Be able to calculate the % of data below / above a value 3) Given the standard deviation and the mean, be able to calculate the percentile for a piece of data 4) Be able to calculate the percent of data between 2 population values

3.5 Z-Scores Ex: Given that X~N(10,2 2 ), what percent of the population is between 7 and 11? Ans: calculate z-scores for the two data values, look up their respective percents in the z-table and subtract for 7: (7 – 10)/2 = -1.5 z = 6.68% for 11: (11-10)/2 = 0.5 z = 69.15% – 6.68 = so 62.47% lies between these two values

3.6 Mathematical Indices These are arbitrary numbers that provide a measure of something e.g. BMI, Slugging Percentage, Moving Average You should be able to work with a given formula and interpret the meaning of calculated results

Review p. 199 #1a, 3a, 4-6