Ch 2 pt 3 - More on Central Tendency

Question 1

Normal distribution

Answer 1

The mean, median and mode coincide in a normal distribution (all their values will be the same)

Question 2

Skewed distribution

Answer 2

The mean is pulled toward the tail of the distribution. This is because the mean is more susceptible to extreme values/outliers.

Positively skewed: modemedian>mean

Question 3

Normal distribution

Answer 3

Mean, median and mode all fall under the highest peak in the graph.

Question 4

Symmetrical, bimodal graph

Answer 4

Mean & Median are equivalent because the graph is symmetrical

There are 2 modes, each falling under the highest peaks in the graph.

Question 5

Symmetrical, rectangular distribution

Answer 5

Mean & Median are equivalent because the graph is symmetrical

No mode because there’s no peak

Question 6

Mode

Answer 6

Gives the least amount of info compared to the other measures of central tendency

More subject to fluctuations, since it relies on one value in the data set

Mode may be best choice if data is…

1. nominal: wouldn’t make sense to calculate the median or mean for people’s eye colour, for ex.
2. Discrete variables: for ex, # of children in household
3. Bimodal/multimodal distribution

Question 7

Median

Answer 7

Median may be best choice if…

1. Distribution is skewed/ contains a few extreme scores (mean is too swayed by extreme values)
2. Ordinal data

**Trouble w/ the median: It’s not mathematically calculated, so it’s utility is limited when it comes to using it in other statistical calculations.

Question 8

Mean

Answer 8

Generally preferred if we’re going to perform other statistical analysis

May be best choice if…

1. Data is measured on an interval or ratio scale
2. When the distribution of scores is normal, unimodal & symmetrical (or close to it)

Question 9

Advantages of Mean

Answer 9

1. The most stable measure of central tendency because all scores in a data set are used to calculate it (not true for mode or median). It’s not as affected by addition or deletion of scores as mode and median.
2. Used in many other statistical procedures.