16 – Averages
Why Should I Care?
You can manipulate numbers tell the story you wish to tell. Is this is unethical and evil? Of course! So knowing how others are – or not – using basic tricks of statistics will help you read through the lies. Here are some basic calculations you need to master to understand scientific papers.
Definitions
Central tendency
Frequency
Mean
Median
Mode
Skewed distributions
If the average grade in your RM class is 58%, but the median and mode are 75%, would you say most people are doing well?
In this case, the mean is _________________ the central tendency.
If the average grade in your RM class is 88%, but the median and mode are 65%, would you say most people are doing well?
In this case, the mean is _________________ the central tendency.
Multimodal distributions
Unimodal
Multimodal
AVERAGES
Students handed in their third RM assignment, and here are the results (on 50 pts).
Use the data below to calculate the mean, the median and the mode of the distribution.
- Is the distribution normal or skewed?
- If you were in this class, would you prefer to score over the mean, or over the median?
|
Student |
Grade - Assignment 3 |
Score |
Frequency |
|
|
1 |
20 |
0 |
|
|
|
2 |
48 |
5 |
|
|
|
3 |
22 |
17 |
|
|
|
4 |
50 |
18 |
|
|
|
5 |
37 |
20 |
|
|
|
6 |
47 |
22 |
|
|
|
7 |
36 |
28 |
|
|
|
8 |
17 |
29 |
|
|
|
9 |
39 |
30 |
|
|
|
10 |
42 |
32 |
|
|
|
11 |
33 |
33 |
|
|
|
12 |
18 |
34 |
|
|
|
13 |
18 |
35 |
|
|
|
14 |
29 |
36 |
|
|
|
15 |
5 |
37 |
|
|
|
16 |
42 |
39 |
|
|
|
17 |
32 |
41 |
|
|
|
18 |
28 |
42 |
|
|
|
19 |
0 |
43 |
|
|
|
20 |
30 |
46 |
|
|
|
21 |
41 |
47 |
|
|
|
22 |
35 |
48 |
|
|
|
23 |
37 |
50 |
|
|
|
24 |
41 |
|||
|
25 |
46 |
|||
|
26 |
34 |
|||
|
27 |
41 |
|||
|
28 |
42 |
|||
|
29 |
43 |
|||
|
30 |
47 |
MEAN = sum / n =
MODE = highest frequency =
MEDIAN = middle value =