Chapter 3 Homework Question 1 Notes Mean: average Median: middle number Mode: number that occurs most often If mean > median then it’s right skewed If mean < median then it’s left skewed If the mean and median are approximately equal, it is symmetrical Approximately equal means a difference of less than 1 Do this in excel!
Question 2 Notes Weighted Average Step 1: Find x*f (number of products * frequency) Step 2: Sum the frequencies Step 3: Sum the products (x*f) Step 4: Sum of products divided by sum of the frequencies
Question 3 Note: When outliers are present in the data, the median is often the best choice because it is unaffected by them. Otherwise, either the mean or the median are both accurate measures of central tendency. When the data is categorical, the mode is the best choice when it exists.
Chapter 4 Notes Range = highest value – lowest value Population variance = sum of squared given values – (the sum of the original values squared/number of values) Number of values Standard deviation = square root of the variance
Question 5 Notes Coefficient of variation = (sample standard deviation / sample mean) * 100 Use =STDEV.S( formula in excel to find the sample standard deviation The set with the larger coefficient of variation has more variability (or less consistency)
Question 7 Notes Calculate mean of sample data: 1.Find midpoint (x) for each class 2.Multiply each midpoint by the appropriate frequency (x*f) 3.Sum (x*f) 4.Sum frequencies 5.Sample mean = sum (x*f) / sum frequencies Calculate standard deviation of sample data 1.Find the midpoint – sample mean for each class 2.Take that answer and square it 3.Then multiply it by the appropriate frequency 4.Add the answers for each class together 5.Take that number divided by (sum of original frequencies – 1) 6.Take the square root of that number
Question 8 Notes P = percentile n = number of values Take the number you get for i and round up. That number corresponds to the number in the data set. Example: If i is 2 and the data set (in order from smallest to largest) is: 58 10 12 Then the answer is 8 Because 8 is the 2 nd number in the set
Question 11 Notes Sample covariance: 1. Find the mean of the set of x and the set of y 2. subtract each value from each set from the mean 3. multiply the corresponding answers for #2 [(x-mean of x)*(y-mean of y)] 4. sum those values 5. sum/(N-1) Sample correlation coefficient: 1. use STDEV.S( formula to find the sample standard deviation of each original x and y set 2. use formula: sample covariance / (stdev of x)*(stdev of y) Relationship between x and y Measured by how close the correlation coefficient is to +1 or -1 Correlation coefficient of +1 = positive linear relationship Correlation coefficient of -1 = negative linear relationship