Notes for Homework 13

Notes on residuals, the distance parallel to the y-axis of the points of the data set to the trendline yp 

 

Notes for Homework 12

Notes on correlation and restriction of range

Notes for Homework 11

Notes on the uses of the chi square table

Notes for Homework 10

Notes on proportions between two samples

Notes on averages between two samples - difference of averages and matched pairs

Notes for Homework 9

Normal approximation of binomial distribution

Notes for t-scores and ranges for p-values, used in hypothesis testing
 

Notes for Homework 8

Confidence intervals for proportions

Basics of hypothesis testing

Notes for homework 7

Notes for scales other percent, notably death statistics per 100,000 population

Notes for confidence of victory

Notes for Student's t-scores, the yellow sheet
 

Notes for Homework 6

Notes on Bayesian probability, probabilities of errors given testing positive and testing negative

Note on homework 6: The false positive and false negative formulas should be switched

False positive = eq/(ap + eq)

False negative = ep/(ep + aq)

Notes on the Expected Value of a game

Notes on classic and modern pari-mutuel statements of profit and risk

There is a lot of overlap between the last two links.

Notes for Homework 5

Notes on the Game Show Problem (bottom of long post)

Notes on dependent trials, sampling without replacement

Notes on the birthday problem

Notes on missing rare side effects

Notes for Homework 4

Notes for contingency tables (first post deals with a future topic concerning contingency tables)

Notes for independent trial probabilities
 

Links to posts about look-up tables and the Central Limit Theorem

A link to posts about look-up tables

 A link to posts about the Central Limit Theorem
 

Links to posts about average, standard deviation, z-scores and how to use the TI-30XIIs to create a list

Posts about average (mean)

Posts about standard deviation

Posts about z-scores

Posts about using the TI-30XIIs to create lists and get the important statistics 

Posts about frequency tables

Note: there are a lot of posts about standard deviation and z-scores that go beyond the scope of what we are doing right now. These are topics we will revisit many times throughout the semester. Another way to get information about the outliers using the average and standard deviation is to search the blog for the word "unusually".

Link to posts about five number summary, IQR and the high and low thresholds Frequency tables and finding mean, median and modeStem and leaf plots

Posts about five number summary and the Inter-Quartile Range (IQR)

Posts about Frequency tables, mean, median and mode

Posts about stem and leaf plots

Important dates for Fall 2016

Add and drop dates
Last day to add: Sunday, September 4
Last day to drop class without a "W": Sunday, September 4
Last date to drop class with a "W": Friday, November 8

Holidays
Labor Day: Monday, September 5
Thanksgiving: Thursday, November 24

Test dates
Midterm 1: Thurs., Oct. 6
Midterm 2: Thurs, Nov. 10
Comprehensive Final: Tues., Dec. 13 8:00-10:00 am

The five number summary and frequency tables

Let's say we have the length of a list n. We know how to find the position of the median once everything has been put in order by the formula (n+1)/2. That is because the list starts at position 1 and ends at position n.  Let's see how we can use this to find the positions of Q1, the median of the low half of the data, and Q3, the median of the high half of the data.

Assume n = 27 and the data is in order from low to high. (27+1)/2 = 28/2 = 14, so the median is in position 14.

Q1: The low half of the data is in positions 1 through 13, so (13+1)/2 = 14/2 = 7, and Q1 is in position 7.

Q3: The high half of the data is in positions 15 through 27. (15+27)/2 = 42/2 = 21, and Q3 is in position 21.

Another example when n = 42.

(42+1)/2 = 21.5, so the median is the average of the values in positions 21 and 22.

Q1: The low half of the data is in positions 1 through 21, so (21+1)/2 = 22/2 = 11, and Q1 is in position 11.

Q3: The high half of the data is in positions 22 through 42. (22+42)/2 = 64/2 = 32, and Q3 is in position 32.

Let's see if we can use this information with a frequency table. The first number is the value and the second number is the frequency.

12, 5
11, 4
10, 3
9,  4
8,  2
7,  4
6,  3
5,  1
4,  2
3,  2
2,  2

The sum of the frequencies is 32.  The position of the median is at (1+32)/2 = 16.5, between positions 16 and 17.

In this data set ordered from top to bottom, the positions 1 to 16 have the high half of the data and the positions 17 to 32 have the low half.  All this does is change which quartile is at which position, not the method of finding the quartile.

Q1: The low half of the data is in positions 17 through 32, so (17+32)/2 = 49/2 = 24.5, and Q1 is between positions 24 and 25.

Q3: The high half of the data is in positions 1 through 16. (1+16)/2 = 17/2 = 8.5, and Q3 is between positions 8 and 9.

We now need to find the values in the positions 8 and 9, 16 and 17 and 24 and 25.  Here is the list with the positions added in. An asterisk (*) will mark the important values

12, 5 positions 1 through 5
11, 4 positions 6 through 9 *
10, 3 positions 10 through 12
9,  4 positions 13 though 16 *
8,  2 positions 17 and 18 *
7,  4 positions 19 through 22
6,  3 positions 23 through 25 *
5,  1 position 26
4,  2 positions 27 and 28
3,  2 positions 29 and 30
2,  2 positions 31 and 32

Median: there is a 9 in position 16 and an 8 in position 17. We take the average of 8 and 9 and get 8.5 as the median value.

Q1: The is a 6 in both position 24 and 25. The average of 6 and 6 is 6.

Q3: Likewise, there is an 11 in both position 8 and 9. The average of 11 and 11 is 11.

On this list, it was just a coincidence that the median was not a whole number and the two other quartiles were nice round numbers. Any time a quartile is between two positions, there is a chance it will be the average of two different values.