Descriptive statistics

What is descriptive statistics?

Descriptive statistics are used to summarise data

What is measures of central tendency?

These tell you what the "typical" or "average" value is in the data
➡ This includes: Mean, Median, and Mode

What are measures of dispersion?

These tell you how spread out the data is
➡ This includes: Range and Standard Deviation

What are extreme values or outliers?

An extreme value is a number in the data set that is much higher or lower than all the others.
It doesn’t match the pattern of the rest.

What is the mean?

The mean is the total of all values divided by the number of values.

What are the advantages and disadvantages of the mean?

+ Takes all values into account - It uses every single number in the data set, so it’s very representative if the data is clean.

- Distorted by extreme values (outliers) - One very high or very low number can skew the mean and make it misleading

What is the median?

The median is the middle value in a list of numbers that have been put in order.

What are the advantages and disadvantages of the median?

+ Not distorted by extremist values - even if there’s a very high or very low number, the median stays the same, making it more reliable when data is skewed.

+ Simple and easy to calculate and shows the middle value

- Does not take into account all the values in the data - So it's less representative when data is evenly distributed

What is the mode?

The mode is the value that appears most often in a data set.
Think: “most frequent” or “most common”

What are the advantages and disadvantages of the mode?

+ Simple and easy to calculate

+ Not distorted by extreme values

- There can be multiple modes (bimodal or multimodal) - This makes it less clear and harder to interpret so doesn’t say which value best represents the data.

What is the range

The range is the difference between a data set’s highest and lowest values.

Largest value - smallest value.

What are the advantages and disadvantages of the range?

+ Simple and easy to calculate

- Distorted by extreme values

What is standard deviation?

Standard deviation tells you how much the values in a data set vary from the mean.

• “This data set has a low level of dispersion”
  → (meaning values are close to the mean = low SD)

• “This data set shows high variability”
  → (meaning values are far from the mean = high SD)

What are the advantages and disadvantages of the mode?

+ Less distorted by extreme values - based on average distance from the mean.

- Harder to calculate as you need the mean