2.1. Descriptive Statistics Flashcards
Population mean…
Can be applied to interval and ratio data.
Is affected by all the values in the dataset - therefore any extreme outliers will stretch the mean value.
Sample mean…
A summation of all values we have over the total number of observations.
Sample mean is the mean calculation for a subset of the population.
Grouped data mean…
The frequencies of data are categorised into classes.
We can then use a midpoint value to calculate an fx = (frequency * midpoint value).
The sum of the fx is then divided by the total cumulative frequency.
This type of mean can be calculated for both a population and a sample.
Mean and investments…
The mean is considered a measure of return on investment.
Standard deviation is considered a measure of risk of an investment, as it measures the rate of an investment’s performance.
The greater the standard deviation, the greater the investment’s volatility.
Median of ordered data…
Data must be ordered, from smallest to largest, for example.
The median is the value that divides the ordered sample into two parts, with equal numbers of observations in each part.
Can be applied to ordinal, interval and ratio data (not nominal).
The median is not affected by outliers as we just calculate the midpoint.
There are two ways to calculate the median:
- For an odd sample: (n + 1) / 2 - this is the observation that acts as the median.
- For an even sample: the median is between (n/2) and (n/2 + 1).
Median of grouped data…
Calculate the class interval in which the median observation is held (using the standard calculation method).
Calculate the specific value (check formula on formula sheet).
Mode…
This is the most frequently occuring value in the dataset.
This can be applied to all types of data.
Data can be bimodal, where two values have the highest frequency, or multimodal, where three or more values have the highest frequency.
Choice of measures of central tendencies…
The measure of central tendency that is most appropriate depends on the scenario.
The mean is the most widely used measure of central tendency.
If observations are symmetrical (and unimodal), the mean, median and mode are the same.
Although data can have the same mean, it may be differently distributed (4, 4, 4, 4 and 2, 4, 4, 6).
Additionally, data that have different means can be similarly dispersed (2, 4, 4, 6 and 4, 6, 6, 8).
Quartiles…
Quartiles divide the dataset into four equal parts.
Calculate the class interval in which the lower quartile or the upper quartile is held, using the standard calculation method.
To deduce the 1st and 3rd quartile, divide by either 4 (and then multiply by 3 if applicable).
Range…
The difference between the largest and the smallest observation.
It is the simplest and easiest descriptive statistical measurement to calculate.
It ignores all the data points apart from the most extreme.
Interquartile range can also be calculated if we know both the first and third quartile. This shows the spread of 50% of observations.
Box and whisker plots…
These are used to illustrate the spread of data.
The square shows us how data is concentrated and the whole spread of data is from the ends of the ‘whiskers’.
They are tools that show us the overall distribution of data.
Skewed data can be seen when the median is further to one side or the other.
Mean absolute deviation…
The average of the absolute deviations from the mean.
Looks at dispersion around the central location of the data.
Variance…
A measure that considers all of the information available.
Check formula sheet and tutorial document ‘1.2. Tutorial 1 Answers’ for guidance.
Standard deviation…
The square root of the variance.
We can calculate standard deviation for a population, a sample or for grouped data.
Coefficient of variation…
A measure of relative dispersion (independent of units of measurement).
Considers how the data varies with the mean and standard deviation.
