Advanced Math Topics 3 3 Measures of Central

Advanced Math Topics 3. 3 Measures of Central Tendancy

Measures of Central Tendency * Mean = x (x bar) or μ (“mu” pronouned “mew”) = * Sample Mean for x 1, x 2, …xn = x = * Population Mean = μ = Σx N Sum of all #’s Total Freq. Σx 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. Which do you think is the most meaningful? Why are they called measures of central tendency?

1) G. E. sampled 60 light bulbs for their length of life. Find the a) sample mean, 2) b) median, and c) mode of the grouped data. Σ xf a) Sample Mean of Grouped Data = x = Σf Bulb Life f (hrs. ) Class Mark(x) Class mark • class frequency Total frequency x • f Σ xf = 4740 = Σf 60 79 40 -49 5 44. 5 222. 5 50 -59 7 54. 5 60 -69 8 70 -79 9 64. 5 74. 5 80 -89 12 84. 5 381. 5 b) Median = class mark of the middle frequency 516. 0 The frequency is 60 so the 30 th and 31 st numbers 670. 5 will tell us the median. = 84. 5 1014 90 -99 9 94. 5 100 -109 6 110 -119 4 104. 5 114. 5 60 850. 5 c) Mode is in the 80 -89 interval. 627. 0 We are assuming that each bulb lasted as long as its 458. 0 class mark, which does introduce some error but the 4740 error will be minimal due to the size of the sample.

2) Eddie Gadel is trying to figure out his grade in Geometry. The grades are weighted. What is his overall grade? x • w Weighted sample mean 100 Grade Weight Homework 100 1 Homework 50 1 Homework 100 1 Quiz 60 6 Quiz 77 6 Quiz 75 6 Quiz 82 6 84 6 Test 67 10 Test 65 10 Test 74 10 Test 77 10 Test 82 10 Final 60 20 770 820 1200 105 7468 100 50 0 100 360 462 450 492 504 670 650 740 = 7468 = 105 number • its weight Σ xw =x= Σ w Sum of all weights 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. ”

HW P. 119 #2 -6, 8 -13 skip 11 n Together #8 and #10 Reminder: No name papers. Quiz 3. 1 -3. 3 on Friday n