View
219
Download
1
Category
Preview:
Citation preview
S519: Evaluation of Information Systems
Social Statistics
Ch2: Mean
This week
Mean Median Mode
What is average
Once the data are collected, next step is how to organize the data What is the central tendency of your data
Average (group of data can be summarized by average)
Average is the one value that best represents an entire group of scores Mean Median Mode
Mean
n
XX ___
(x bar): the mean
: sum of the data
: number of the data
___
X
X
n
Calculate mean
Location Number of annual customers
Lanham Park Store 2150
Williamsburg Store 1534
Downtown Store 3564
The mean or average number of shoppers in each store?
Using Excel to do that• use your own formula• use AVERAGE function
Mean
The sample mean is the measure of central tendency which can approximate the population mean
The mean is very sensitive to extreme scores It can put the mean in some extreme direction Make it less representative Less useful as a measure of central tendency
Weighted mean
See Table9.10 (D-p175)
Do it in Excel
Median
It is defined as the midpoint in a set of scores 50% of the scores fall above and one half fall
below.
Calculate median
Odd number of data Rank them Median=middle one Example: 10, 9, 8, 7, 5 (median=8)
Even number of data Rank them Median= sum of two middle data/2 Example: 10, 9, 8, 7, 6, 5 (median=(8+7)/2=7.5)
Median in Excel
Calculate the median of income level
Median
The median is insensitive to extreme cases, where the mean is not.
To measure the central tendency: Have some extreme data, using median No extreme data, using mean Example: 14, 3, 2, 1, (mean=5, median=2.5)
Which represents better the central tendency?
Mode
The mode is the value that occurs most frequently. Calculate the frequency of all the values in a
distribution The value that occurs most often is the mode
Calculate mode
300 students:
Student distribution Number or frequency
American student 150
Asian student 30
European student 5
Mode = american student
Summary
The mean is the middle point of a set of values,
The median is the middle point of a set of cases
The median cares about how many cases, not the values. So the extreme values don‘t count.
When to use what
Mean: No extreme scores and are not categorical
Median Extreme scores and you do not want to distort the
average Mode
Data are categorical in nature and values can only fit into one class
E.g. hair color, political affiliation, religion
Descriptive Statistics in Excel
Take Figure2.9 (S-p57), input these figures to Excel
Data data analysis data analysis box choose Descriptive Statistics tick “labels in first row” output range=c1 tick “summary statistics” click “OK”
Descriptive Statistics
Income Level Income Level$135,456
$54,365 Mean 53324.16667$37,668 Standard Error 16887.71824$34,500 Median 36084$32,456 Mode #N/A$25,500 Standard Deviation 41366.2926
Sample Variance 1711170163Kurtosis 4.861219327Skewness 2.173756462Range 109956Minimum 25500Maximum 135456Sum 319945Count 6
Exercise 1 (S-p62)
Calculate mean, median and mode for the following data:
Score1 Score2 Score33 34 1547 54 1675 17 1324 26 1455 34 1546 25 1457 14 1138 24 1566 25 1545 23 123
Exercise 2 (S-p62)
Writing a sale report to your boss according to the figures of things sold today:
special Number Sold costHuge Burger 20 $2.95 Baby Burger 18 $1.49 Chicken Littles 25 $3.50 Porker Burger 19 $2.95 Yummy Burger 17 $1.99 Coney Dog 20 $1.99
Exercise 4 (S-p63)
Calculate the average sale
toy Julysale AugustSale SeptemberSaleslammer 12345.00 14453.00 15435.00radar zinger 31454.00 34567.00 29678.00lazertags 3253.00 3121.00 5131.00
Exercise 5 (S-p63)
Patient record Mean and median, which is better for what?
12/1-12/7 12/8-12/15 12/16-12/230-4 years 12 14 155-9 years 15 12 1410-14 years 12 24 2115-19 years 38 12 19
Stat Homework 1
S-p62‐63: 2, 4, 5 Due Jan 28 – week3 How to submit:
Softcopy: Oncourse Print copy:
write your name, email, and S519 in the first page Submit to me during the class – week 3 (Jan 28)
Recommended