HCI-AOS Statistics Module 2010
BASIC STATISTICS HOMEWORK 1
Description of data
A. Measures of central tendency
Description of the location of the “centre” of a set of data
The measures of central tendency are mean, median and mode.
Measure of
central tendency
Mean
Median
Mode
What it is
How to obtain value
Arithmetic average
of a set of scores
Add up scores and divide by number of
scores
Mid-point of a set of
ordered scores
Arrange scores from lowest to highest.
The median is the middle value for an
odd number of scores; and the mean of
the two middle values for an even
number of scores
The most frequent
value in a set of
scores
Choose the score that occurs at the
highest frequency
Figure 1
Symmetric (normal) and Skewed Distributions
http://www.developer.com/mgmt/article.php/11085_3621006_4
Practice 1
3. Work out the (a) mean; (b) median; and (c) mode of the data you have collected.
(a) Mean
(b)Median
(c) Mode
Height /cm
Thumb Length /mm
Text Time /s
Sum of 2 Virtual Die roll
SMTP Research Module 2010 / Developed by D Writer, LeeTK & J Loh
With resources contributed by YipCW
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3. Microsoft Excel: Step by Step
The following is an example of how to find the mean, mode and median using MS Excel.
Enter the numbers in cells A2 to A16:
104, 104, 104, 104, 104, 107, 109,
109, 109, 110, 109, 111, 112, 111,
109
For the mean,
enter =AVERAGE(A2:A16) in a blank
cell.
For the mode,
enter =MODE(A2:A16) in a blank cell.
For the median,
enter =MEDIAN(A2:A16) in a blank
cell.
Figure 2 – Example of data entry
Perform the same operations using the data you have collected in
MS Excel.
SMTP Research Module 2010 / Developed by D Writer, LeeTK & J Loh
With resources contributed by YipCW
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B. Measures of spread of data
The standard deviation is a measure of the spread of data about their mean.
According to the Rounding Rule for the Standard Deviation, the final answer should
be rounded to one more decimal place than that of the original data.
If the distribution
 About 68% of
 About 95% of
 About 99% of
of the data is symmetric, then the following rules apply:
all scores fall between the mean () and 1 standard deviation ().
all scores fall between the mean and 2 standard deviations.
all scores fall between the mean and 3 standard deviations.
Figure 3 – Interpretation of standard deviation on a normal distribution
http://www.answers.com/topic/normal-distribution
Practice 2
1. Using MS Excel to compute standard deviation
Example (Refer to Figure 4)
Enter the numbers in a range A2:A7. For the sample standard deviation, enter in a
blank cell =STDEV(A2:A7).
Figure 4 – Example of data entry and finding standard deviation
2. Use MS Excel to find the standard deviation for the data you have collected in the
table below.
2a. Using the standard deviation that you have computed, measure the percentage of
data points that fall within 1,2 and 3 standard deviations from the mean values.
Record these percentages in your data table.
SMTP Research Module 2010 / Developed by D Writer, LeeTK & J Loh
With resources contributed by YipCW
3
Standard Deviation
(SD)
% of data
within 1 SD
from mean
% of data
within 2 SD
from mean
% of data
within 3 SD
from mean
Height /cm
Thumb Length
/mm
Text Time /s
Sum
of
2
Virtual Die roll
2b. Compare your percentage of data points within 1 standard deviation to percentage in
Figure 3. Do likewise for 2 and 3 standard deviations.
2c. How would you be able to make your percentage of data within 1 standard deviation
closer to the model in Figure 3?
SMTP Research Module 2010 / Developed by D Writer, LeeTK & J Loh
With resources contributed by YipCW
4