1. MDM4U Chapter 3 Review Normal Distribution Mr. Lieff

2. 3.1 Graphical Displays name and be able to interpret the various types of distributions ex: When would we use a histogram vs. a bar graph? Histogram  Continuous data  Discrete data with a large spread (>20) Bar graph  qualitative data ex: How do you calculate bin width? (range) ÷ (# of bars)

3. 3.2 Central Tendency Be able to calculate mean, median, mode and weighted mean Determine which measure is appropriate Mean if no outliers Median if outliers Mode for qualitative data; when frequency is most important Recognize the location of the measures with respect to skewed distributions if mode < median < mean (right skewed) If mean < median < mode (left skewed)

4. 3.3 Measures of Spread Be able to calculate and interpret range, IQR and standard deviation A larger value for any measure of spread (range, IQR, std.dev.) means the data has more spread Range  size of the interval containing all of the data IQR  size of the interval containing middle 50% of the data Std dev measures the average variation from the mean (of the data)

5. 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 How to calculate Std.dev. Find the mean Find the deviations (data point – mean) Square the deviations Average the deviations  variance σ 2 Take square root  std. dev. σ OMLUD* * = credit to Chris, Jasmine, Holly

6. 3.4 Normal Distribution Be familiar with the characteristics of a Normal Distribution (68–95–99.7% rule) Calculate the % data based on 1, 2 or 3 standard deviations above 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)

7. Normal Distribution 34% 13.5% 2.35% 68% 95% 99.7% 101214168 6 4 0.15%

8. 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% + 13.5% = 81.5%

9. 3.5 Z-Scores Standard normal distribution mean 0, std dev 1 1) Be able to calculate a z-score 2) Be able to calculate the % of data below / above a value (z-table on p. 398) 3) Given the standard deviation and the mean, be able to calculate the percentile for a piece of data (round z-table percentage to whole number) 4) Be able to calculate the percent of data between 2 population values (find z-scores, look up %s below, subtract smaller from larger)

10. 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: z = (7 – 10)/2 = -1.5 => 6.68% for 11: z = (11-10)/2 = 0.5 => 69.15% 69.15 – 6.68 = 62.47 so 62.47% of the data lies between these two values

11. 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 Moving averages – use for data that fluctuates over time

12. Review p. 199 #1a, 3a, 4-6 20 Marks MC 30 marks Short Answer / Problem You will be provided with: Formulas in Back of Book z-score table on p. 398