Measures of Central Tendency Section 5.1 Standard: MM2D1 bc Essential Question: How do I calculate and use measures of central tendency and dispersion to compare data sets?

Statistics: numerical values used to summarize and compare sets of data Mean: average, denoted by Median: the middle number when the numbers are in order Mode: the number or numbers that occur more frequently Measures of dispersion: a statistic that tells you how spread out the data values are Range: the difference between the greatest and least data values Standard deviation: the measure that describes the typical difference between a data value and the mean, denoted by σ Interquartile range: the difference between the upper and lower quartile of a set of data Variance: standard deviation squared.

Find the following. 1. 42, 78, 56, 95, 49, 55, 63, 71 Mean: _______ Median: _______ Mode: _______ Range: _______ Q1: _______ Q2: _______ Q3: _______ IQR: _______ 63.63 42 + 78 + 56 + 95 + 49 + 55 + 63 + 71 = 509 509/8  63.63 59.5 42, 49, 55, 56, 63, 71, 78, 95 none 53 95 – 42 Q1 (49 + 55)/2 52 Median (56 + 63)/2 59.5 Q2 Q3 (78 + 71)/2 74.5 52 59.5 74.5 22.5 74.5 – 52

Standard deviation of population σ (read as “sigma”) of x1, x2, …, xn is: Now find the standard deviation of example 1: 42, 78, 56, 95, 49, 55, 63, 71

Standard Deviation on the Calculator: 2nd DATA ENTER (1-VAR) DATA Input data into x1, x2, x3, … Use to move to next data entry Notice there is a FRQ after each xn term. This is means frequency. If a number appears in the list more than once you may change this to the number of times the number appears in the list. STATVAR n = number of terms • = mean Sx = sample stand. dev. • σx = population stand. dev. Σx = sum of data • Σx2 = sum of data squared

2. 15, 11, 15, 14, 14, 13, 17 Mean: _______ Median: _______ Mode: _______ Range: _______ Q1: _______ Q2: _______ Q3: _______ IQR: _______ Standard deviation: _______ Variance: ______ 14.14 15 + 11 + 15 + 14 + 14 + 13 + 17 = 99 99/7 = 14.14 14 11, 13, 14, 14, 15, 15, 17 14, 15 6 17 – 11 Q1 13 Median 14 Q2 Q3 15 13 14 15 2 15 – 13 1.73 2.98 (Standard deviation)2

Draw a box and whisker plot for the data set. Now check for outliers. (Remember: 1.5 • IQR) 10 11 12 13 14 15 16 17 18 19 20 1.5(2) = 3 Q3 + 3 = 15 + 3 = 18 (No values larger than 18) Q1 – 2 = 13 – 3 = 10 (No values smaller than 10) Therefore, no outliers.

3. Compare the means and standard deviations of Set A and Set B. Set A mean: _______ Set B mean: _______ standard deviation: _______ standard deviation: _______ Set A 7 3 4 9 2 Set B 5 8 6 5 6 2.6 1.4 Set B has a higher average and Set A’s data is more spread out.

4. The lists show the number of cars sold each month for one year by two competing car dealers. Compare the mean and standard deviation for the numbers of cars sold by the two car dealers. Dealer A: 8, 9, 15, 25, 28, 16, 24, 18, 21, 14, 16, 10 Dealer B: 7, 4, 10, 18, 21, 30, 27, 20, 16, 18, 12, 9 Dealer A mean: _______ Dealer B mean: _______ standard deviation: _______ standard deviation: _______ 17 16 6.2 7.6 Dealer A sells more cars on average and Dealer B’s data is more spread out.