Statistics Class 4

1. Statistics Class 4 January 30th, 2012

2. Group Quiz 3 Heights of statistics students were obtained by the author as a part of  a study conducted for class.  The last digits of those heights are listed below.  Construct a frequency distribution and then a histogram.  Based on the distribution, do the heights appear to be reported or actually measured?  What do you know about the accuracy of the results? 0 0 0 0 0 0 0 0 0 1 1 2 3 3 3 4 5 5 5 5 5 5 5 5 5 5 5 5 6 6 8 8 8 9

3. Measure of center A measure of center is a value at the center or middle of a data set. The mean of a set of data is the measure of center found by adding the data values and dividing the total by the number of data values. =average(data)

4. Calculate the mean of some data 76 64 72 80 88 76 60 76 72 76 68 80 80 104 64 88 68 60 68 76 80 72 76 72 68 88 72 80 96 60 72 72 68 88 72 88 64 124 80 64

5. Calculate the mean of some data 76+64+72+80+88+76+60+76+72+76+68+80+80+104+64+88+68+60+68+76+80+72+76+72+68+88+72+80+96+60+72+72 +68+88+72+88+64+124+80+64 = 3052 x= 3052/40=76.3

6. Median The median of a data set is the measure of center that is the middle value when the data values when arranged in increasing (decreasing) order. So take  76 64 72 80 88 76 60 76 72 76 68 80 80 104 64 88 68 60 68 76 80 72 76 72 68 88 72 80 96 60 72 72 68 88 72 88 64 124 80 64 order it 60 60 60 64 64 64 64 68 68 68 68 68 72 72 72 72 72 72 72 72 76 76 76 76 76 76 80 80 80 80 80 80 88 88 88 88 88 96 104 124  

7. Median Select the middle values 60 60 60 64 64 64 64 68 68 68 68 68 72 72 72 72 72 72 72 72 76 76 76 76 76 76 80 80 80 80 80 80 88 88 88 88 88 96 104 124 Even number of data values average the middle two. (72+76)/2=148/2=74

8. Mode The mode of a data set is the data value that occurs with greatest frequency. When two data values occur with the same greatest frequency, each one is a mode and the data set is bimodal. No repeated data value, then there is no mode. Find the mode of our previous data 60 60 60 64 64 64 64 68 68 68 68 68 72 72 72 72 72 72 72 72 76 76 76 76 76 76 80 80 80 80 80 80 88 88 88 88 88 96 104 124 

9. Mode The mode of a data set is the data value that occurs with greatest frequency. When two data values occur with the same greatest frequency, each one is a mode and the data set is bimodal. No repeated data value, then there is no mode. Find the mode of our previous data 60 60 60 64 64 64 64 68 68 68 68 68 72 72 72 72 72 72 72 72 76 76 76 76 76 76 80 80 80 80 80 80 88 88 88 88 88 96 104 124  Mode is 72.

10. Midrange The midrange of a data set is the value midway between the maximum and minimum values midrange=(maximum data value + minimum data value)/2 From our previous data set the max was 124 and the min was 60 so.... midrange= (124 + 60)/2=62.

11. What do you need on the final? Suppose you are in a class, where your grade depends on 4 tests each worth 100 points. Let’s say you earned a 95 on the first test, a 91 on the second test, and a 81 on the third test. What grade must you earn on the final test to receive an A (a mean test score of a 90)?

12. Mean from a frequency distribution • is the estimate of the mean from grouped data “a.k.a a freq. Dist.” • frequency of each class/bin • midpoint of each class/bin • sum of the products (multiplication) of the each midpoint and its frequency • total of the frequencies

18. You try! Estimate the mean of the frequency Distribution Below

19. Homework 3-2: 1, 3, 5-19 odd,21,29,31