1. Advanced Math Topics 3.3 Measures of Central Tendancy

2. Measures of Central Tendency * Mean = x (x bar) or μ (“mu” pronouned “mew”) = Sum of all #’s Total Freq. * Sample Mean for x 1, x 2, …x n = x = * Population Mean = μ = Σ x n N the total population frequency Generally speaking, Greek letters refer to a population and English letters refer to a sample. * Mode = the number that occurs MOST frequently * Median = the middle number when the numbers are in order. If there is an even number of values, find the mean of the middle two values. Why are they called measures of central tendency? Which do you think is the most meaningful?

3. a) Sample Mean of Grouped Data = x = Σ xf Σ f Class mark class frequency Total frequency 1)G.E. sampled 60 light bulbs for their length of life. Find the a) sample mean, b) median, and c) mode of the grouped data. Bulb Life (hrs.) f 40-495 50-597 60-698 70-799 80-8912 90-999 100-1096 110-1194 Class Mark(x) 44.5 54.5 64.5 74.5 84.5 94.5 104.5 114.5 x f 222.5 381.5 516.0 670.5 1014 850.5 627.0 458.0 60 4740 Σ xf Σ f = 4740 60 = 79 b) Median = class mark of the middle frequency The frequency is 60 so the 30 th and 31 st numbers will tell us the median. = 84.5 c) Mode is in the interval. We are assuming that each bulb lasted as long as its class mark, which does introduce some error but the error will be minimal due to the size of the sample. 80-89

4. 2) Eddie Gadel is trying to figure out his grade in Geometry. The grades are weighted. What is his overall grade? GradeWeight 1001 1001 501 01 1001 606 776 756 826 846 6710 6510 7410 7710 8210 6020 Homework Quiz Test Final Homework Quiz Test Weighted sample mean = x = Σ xw Σ w number its weight Sum of all weights xw 100 100 50 0 100 360 462 450 492 504 670 650 740 770 820 1200 7468105 = 7468 105 = 71.12% Sometimes it can be tough to figure out which number to divide by. It helps to think like this… “If we are finding miles per gallon then we will divide by the total number of gallons” or “If we are finding price per car, then we will divide by the number of cars.”

5. HW P. 119 #2-6, 8-13 skip 11 P. 119 #2-6, 8-13 skip 11 Together #8 and #10 Reminder: No name papers. Together #8 and #10 Reminder: No name papers. Quiz 3.1-3.3 on Friday Quiz 3.1-3.3 on Friday