Frequency distribution

Question 1

What are summary statistics?

Answer 1

Mean, median, mode

- describe typical performance (avg)

Question 2

What are frequency distributions?

Answer 2

Describe prevalence of different types of performance

• quantitative
• -> frq of single variable: How many people did well
• qualitative
• -> Frq of mutually exclusive categories: How many ppl like R, Q or T?

Question 3

Describe grouped frq distribution

Answer 3

• data collected sorted into a specific interval width = group
• groups do not overlap!!
• bar graph
• a trade off between loss of info + being able to see patterns

Question 4

Describe cumulative frq distribution

Answer 4

1. Raw data = total in each cell
2. Cumulative frq = each cell total + all precedings cell totals
3. Cumulative frq = cum.frq as % of total
   = line graph

Question 5

Describe relative frq distribution

Answer 5

• useful for comparing groups with different totals

= (cell total/ overall total) x 100

Question 6

What is the difference between raw frq and relative frq distribution on the graph?

Answer 6

• only the scale of the graph changes, not the pattern of frq

Question 7

What is the normal distribution?

Answer 7

• Normal curve = mathematical abstraction which conveniently describes many frq distribution of scores in rl

Question 8

What are the properties of the normal distribution?

Answer 8

• bell-shaped + asymptotic at extremes
• symmetrical around the mean
• mean, median + mode all have the same value

Question 9

What are skewed distributions?

Answer 9

lack symmetry around the central point

• left lean = positive skew
• right lean = negative skew

Question 10

How doe skews distort interpretations of mean performance?

Answer 10

• RT often show positive skew
• SAY typical performance = 200-300ms
• BUT mean would be much higher because of the disproportionate effect of long RT (outliers)

Question 11

How could we deal with outliers distorting means?

Answer 11

• use median instead?
• OR principle treatment of outliers
• -> “trimmed mean” = delete top 5% of scores

Question 12

What does kurtosis mean?

Answer 12

is the measure of all the “tail-heaviness” of all distribution

Question 13

What are different kurtosis distributions?

Answer 13

• like normal: Mesokurtic distribution
• Positive/ high kurtosis = leptokurtic distribution = more outliers = BAD
• Negative/ low kurtosis = platykurtic distribution = fewer outliers = thinner tails