Central Tendency

Question 1

Central tendency

Answer 1

A summary measure that attempts to describe a whole set of data with a single value that represents the centre of its distribution

Mode / Mean / Median

Question 2

Mode

Answer 2

most frequent value or score

pros:
easy to calculate and understand
only option with nominal data; useful for most popular answer

cons:
ignores most of your data set
strongly affected by sampling variation

Question 3

Mean

Answer 3

x̅ (sample); μ (population)
sum of all scores divided by the total number of scores; fulcrum/balancing point of all scores
∑X / N

pros:
least affected by sampling variation

cons: most affected by extreme scores and skew

Question 4

Median

Answer 4

the score that is exactly in the middle (half of the other scores are higher, half are lower)
for even number of scores, the two centremost are averaged to get the median

equivalent to 50th percentile point (P50)

(N+1) / 2

Question 5

Outliers

Answer 5

highly atypical scores

solutions:
- report the median
- report the mean with outliers removed (common if source of outlier is suspected to be measurement error)

Question 6

Overall mean

Answer 6

x̅ overall = sum of all scores / N

ie, ∑X / N
or, ∑X = Nx̅