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```Lesson 5
QUANTITATIVE DATA ANALYSIS
Central tendency
Which measure of central
tendency should be
used?
5 QUESTIONS
Complete the 5 questions on the
sheet
Standard deviation

What does this describe?

How do we work this out?

Step 1?

Step 2?

Step 3?

Step 4?

Step 5?
Standard deviation
1. Work out the
mean of the results
first
2. Find this for
each value
numbers together
4. Divide total
amount by n-1
5. Take the
square root of
Standard deviation
Score on memory test (male)
14
12
12
13
10
16
Calculate SD to
3 significant figures
How can standard deviation help
you understand results?

Why is standard deviation used instead of the range?

Better measure of spread as it less affected by extreme values

Takes all of the scores into account

These are scores from a memory test

Comment on these results in pairs – feedback to class

Female average score was higher than male

Female SD higher that males – meaning their scores were more
spread out than males and therefore the scores were less consistent
and more varied.
Normal and
Skewed Distribution
Normal and skewed distribution

Small samples – central tendency and standard deviation  useful statistics

Larger samples – useful to examine overall distribution formed by the data

Examining distributions can show trends in the data and we can estimate the
distribution of scores in the whole population
Normal and Skewed Distribution

If mean, median and mode are the same/similar and focus around the middle set
of scores (median) then there is normal distribution

Multi-modal (more than one mode)– not normally distributed

When mean, median and mode are not similar – distribution will be skewed

Data is mainly above mean – negative skew – Mode> median < Mean

Data is mainly below mean – positive skew – Mean> median> mode
Normal Distribution
Mean=Median=Mode

Bell shaped curve

Mean, median and mode should be
aligned around the mid -point

Tail ends shouldn’t meet the horizontal
axis

We can estimate the % of people that
fall under the curve at each standard
deviation

68% of the population fall between one
standard deviation and 2 standard
deviations etc….
Distribution – only considered for interval
data (have known scores)
So that mathematical calculations can be
carried out
Ordinal
Interval
Nominal
Categories. This is simply putting items together
without ordering or ranking them. E.g. obedient or
not obedient e.g. tallies are made when observing
behaviour
Elements of the data describe properties of objects or events that are
ordered by some characteristic (e.g. Rating on a scale of 0-10 for
attractiveness where 0 is less attractive and 1- is attractive?) The order of
the objects does not, however, provide any information about the distance
along the continuum between any two adjacent items.
Actual scores that are mathematical in having equal
intervals between the so that calculations can be
conducted. E.g. reaction times, number of words recalled.
age, height.
Ordinal. Elements of the data describe properties of objects or events that
are ordered by some characteristic (e.g. Rating on a scale of 0-10 for
attractiveness where 0 is less attractive and 1- is attractive?) The order of
the objects does not, however, provide any information about the distance
along the continuum between any two adjacent items.
Interval. Actual scores that are mathematical in having
equal intervals between the so that calculations can be
conducted. E.g. reaction times, number of words recalled.
age, height.
Nominal. Categories. This is simply putting items
together without ordering or ranking them. E.g.
obedient or not obedient e.g. tallies are made
when observing behaviour
Link to other side of the
course – which statistical
test would you use for this
type of data?
Behaviour observed on bus
Tally (frequency)
Giving up seat
1111
Not giving up seat
11
Examples:
TIME OF DAY on a 12-hour clock
RELIGIOUS PREFERENCE: 1 = Buddhist, 2 = Muslim, 3 =
Christian, 4 = Jewish, 5 = Other
POLITICAL ORIENTATION: Left, Center, Right
Examples:
LEVEL OF AGREEMENT: No, Maybe, Yes
MEAL PREFERENCE: Breakfast, Lunch, Dinner
POLITICAL ORIENTATION: Republican, Democratic,
Libertarian, Green
POLITICAL ORIENTATION: Score on standardized scale of
political orientation
RANK: 1st place, 2nd place, ... last place
Video - draw out with video and
make notes

? Positive or negative? Why?
Label where the
mode median
and mean would
be

Imagine it is a whale!

Whale swimming towards vertical axis – coming home positive 

Away from vertical axis – leaving home negative 
?
Label where the
mode median
and mean would
be
?
?
?

Question 1

1. Work out the mean, median and mode for each set of scores (3
marks)

2. Is the set of scores for the ‘sound alike’ condition normally
Task 2 – complete questions 1,2
and 3 of the sheet

Participants in a memory study were tested on their recall of a list of
15 words.

Mean number of words recalled was 10

Median was 11

And the mode was 15

a. Sketch a graph showing he most likely distribution curve for the
results.

b. What type of distribution is shown on your graph?
```
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