Central Tendency and Z Scores

Question 1

What is the mean?
What are the advantages and disadvantages of the mean?

Answer 1

Sum of all data points divided by number of observations. Also know as the “average” or “arithmetic mean”
Should only be used on interval or ratio data.
Advantages - Used all values, is sensitive
Disadvantages- Outliers can affect the mean

Question 2

What is the median?
What are advantages and disadvantages of the median?

Answer 2

Middle data value when data is sorted from ascending/descending order.
Can be used on interval, ratio, and ordinal data
Advantages - Not affected by outliers
Disadvantages - Does not use all data, not very sensitive

Question 3

What is the mode?
What are the advantages and disadvantages of the mode?

Answer 3

Data value that occurs with the greatest frequency
Can be used on nominal data
Advantages - The only measure that can be used for categorical data
Disadvantages - Possible to have more than one mode or no mode - not very useful

Question 4

What are the properties of a “normal” distribution?

Answer 4

• Symmetrical
• Unimodal
• The mean, median and mode are at the centre of the peak
• 68% of scores within 1 standard deviation (± 1 SD), 95% within ± 2 SD, 99.7% within ± 3 SD
• Shape of the curve determined by the mean and the SD
• Kurtosis of 3 (mesokurtic)

Question 5

What is kurtosis? What are the three types of kurtosis?

Answer 5

A measure of the tailedness (how often outliers occur) of a distribution
Mesokurtic (normal) - Distributions that are similar peak and tail shape as normal distribution
Platykurtic (less than normal) - Distributions are thin-tailed, meaning they have few outliers. Flat peak
Leptokurtic (more than normal) - More
extreme outliers. Sharp peak

Question 6

What are the types of skew? What does skewness tell us about the direction of outliers?

Answer 6

Positive skew (right-skewed) - More outliers on the right. Most values clustered around left tail of the distribution, while the right tail is longer
Negative skew (left-skewed) - More outliers on the left. Most values on the right tail, left tail is longer

Question 7

What is collective intelligence?

Answer 7

The enhanced capacity that is created when people work together, often with the help of technology, to mobilise a wider range of information, ideas and insights.

Question 8

What are Z scores?

Answer 8

“Standardised scores” - A group pf datapoints transformed to have a mean SD of 1, just like the standard normal distribution.

Question 9

What is a Z score?

Answer 9

Number of standard deviations away from the mean