Quantitative Methods - Data - Measures of Central Tendency

Question 1

what do measures of central tendency identify?

Answer 1

the centre, average of a data set

Question 2

what are the differences between the population mean and sample mean?

Answer 2

the population mean is unique in that a given population only has one mean. the sample mean is a selection of a population and is used to make inferences about the population mean

Question 3

what type of mean are population and sample means examples of?

Answer 3

arithmetic means

Question 4

what is an arithmetic mean?

Answer 4

the sum of the observation values divided by the number of observations

Question 5

what are key properties of an arithmetic mean?

Answer 5

• All interval and ratio data sets have an arithmetic mean.
• All data values are considered and included in the arithmetic mean computation.
• A data set has only one arithmetic mean (i.e., the arithmetic mean is unique).
• The sum of the deviations of each observation in the data set from the mean is always zero.

Question 6

what can have disproportionate influences on the arithmetic mean?

Answer 6

large outliers

Question 7

what are methods to remove outliers when wanting a truer arithmetic mean? how do they work?

Answer 7

trimmed mean - excludes a stated percentage of the most extreme observations

winsorized mean - substituting a value for the highest and lowest observations instead of removing them

Question 8

what does the computation of a weighted mean/average recognise?

Answer 8

that different observations may have a disproportionate influence on the mean

Question 9

what is the median?

Answer 9

the midpoint of a data set when the data is arranged in ascending or descending order

Question 10

when is the median useful?

Answer 10

when there are outliers, the median isn’t affected whereas the mean can be changed significantly

Question 11

how do you calculate the median when there are an even number of observations?

Answer 11

you take the arithmetic mean of the two middle obervations

Question 12

what is the mode?

Answer 12

the most commonly occuring observation in a data set

Question 13

what are terms used to describe when a data set has 1 mode, 2 modes and 3 modes?

Answer 13

unimodal, bimodal and trimodal

Question 14

when is a geometric mean commonly used in investing?

Answer 14

when calculating investment returns over multiple periods or when measuring compound growth rates

Question 15

when would you use a weigthed mean?

Answer 15

when certain values in a data set are more important than others

Question 16

what is the harmonic mean?

Answer 16

it’s the reciprocal (inverse) of the arithmetic mean of individual observations

Question 17

when is the harmonic mean appropriate to use in finance?

Answer 17

when averaging things like rates/costs per shares etc.

• helps to find multiplicative or divisor relationships between fractions without worrying about common denominators

Question 18

What are appropriate uses of the following definitions of these means?

Arithmetic mean
Geometric mean
Trimmed mean
Winsorized mean
Harmonic mean

Answer 18

Arithmetic mean - Estimate the next observation, expected value of a distribution.
Geometric mean - Compound rate of returns over multiple periods.
Trimmed mean - Estimate the mean without the effects of a given percentage of outliers.
Winsorized mean - Decrease the effect of outliers on the mean.
Harmonic mean - Calculate the average share cost from periodic purchases in a fixed dollar amount.