# Quantitative Methods - Summary Data Flashcards

What is the purpose of location measures to an investment manager?

Indicate the central/long run average value/return achieved

What does the dispersion measure indicate to the investment manager?

The variability or spread of values around this point

What are the three methods of presenting data?

Raw data

Tabulated data

Grouped data

What is raw data?

Data presented as a simple list of figures or values that may or may not be ordered

For what is tabulating data good for?

Summarising lagged volumes of discrete data

What is grouped data often used for?

To summarise continuous data

What are the four location measure?

Arithmetic mean

Median

Mode

Geometric mean

What is the arithmetic mean?

Simple average calculated by adding up the observed values and dividing by the number of observed values

How do you calculate the arithmetic mean fro tabulated data?

If the same number appears multiple times, you multiply it but the number of time it appears

What is a weighted average useful for?

Determining the return on a portfolio of securities

How do you calculate the wedged average?

Work out what proportion each return represents then multiple the return by the proportion. Add the results of these together

What must be done the calculation of the arithmetic mean for grouped data?

One must make the assumption that values are evenly spread within each range so we can, therefore, evaluate each range based on its midpoint

What is a problem with the arithmetic mean?

Since all observed values are considered, this measures can be severely distorted by extreme values

What is the median?

The value of the mid-item in an ordered arrangement of the observed data

What occurs if there are an even number of items in the calculation of the median?

An average would be taken from the value above and the value below

How do you work out the median for grouped data?

Assuming the items within the range are evenly spread the median is the number into the band divided by the frequency of the band

What is the general expression for working out the median of grouped data?

Median = start value of band + fraction of distance through band * width of band

What is the formula for the median of grouped data?

Median = start value of band + (median number - cumulative number to start the band/ number of items in band * width of band)

What is different about the median compared to the mean?

It will not be affected by the size of extreme values, however it will be affected by the addition of extreme items since the total number of observed values will change

What is the mode?

The most frequently occurring item in the observed data on the basis that the more central items should occur most frequently in a Normal distribution

What happens when determining the mode for grouped data?

One cannot establish a single value within this range since we assume that the items are evenly distributed throughout the range, hence all are equally likely. This means we have a modal range over 5-9.9 rather than a single figure

What are some key different between the mode and the median and mean?

The mode must be an actually occurring number.

There may be several modes meaning the mode may be of limited value as a central measure since, in extreme cases, it gives little or no indication of central tendency

Since it is the most frequently occurring item, it is unaffected by extreme values

How is the geometric mean calculated?

It is calculated by taking the nth route of the product of the n observed values