Descriptive statistics

Descriptive statistics

What are the types of descriptive statistics?

• Measures of central tendency

• Measures of dispersion

Descriptive statistics - measures of central tendency

What are Measures of central tendency (+ examples)?

A single value that summarises a set of data by identifying the typical value of the data set → the average

• Mean

• Median

• Mode

Descriptive statistics - measures of central tendency

What is the mean?

Arithmetic/mathematical average (add together, then divide by amount of numbers)

Descriptive statistics - measures of central tendency

What are the strengths of using mean?

Makes use of all values → SO most sensitive measure of central tendency

Descriptive statistics - measures of central tendency

What are the weaknesses of using the mean?

bcs includes all values, can be affected by outliers/anomalies + give a misleading answer

Descriptive statistics - measures of central tendency

What is the median?

If you line the data in order from smallest, to biggest – the middle value is the median

Descriptive statistics - measures of central tendency

When can you use the median?

• interval data

• ordinal data

Descriptive statistics - measures of central tendency

What are the strengths of using the median?

• Unaffected/not distorted by extreme values

• Easy to calculate

Descriptive statistics - measures of central tendency

What are the weaknesses of the median?

• Not as 'sensitive' as the mean because it doesn't use all data

• If there is an even number of data points → the ‘typical’ value will be a number that is not one of the recorded values (unlike mode)

Descriptive statistics - measures of central tendency

What is the mode?

The most common value/item in a data set

Descriptive statistics - measures of central tendency

what are the strengths of the mode?

• Unaffected/not distorted by extreme values

• more useful for discrete data → eg: makes more sense to say the average family has 2 children vs 1.8 children

• the only method that can be used when data is in categories (nominal data)

Descriptive statistics - measures of central tendency

What are the weaknesses of the mode?

• Not useful for describing data when there are multiple/no modes → esp likely in small data sets → SO in some cases doesn’t give an exact average value

• Tells use nothing about other values in a distribution bcs doesn’t include all values → not as sensitive as the mean when measuring central tendencies

Descriptive statistics - measures of dispersion

What are measures of dispersion?

A single value that summaries how spread out the individual scores are in a data set

• Rage

• Standard deviation

Descriptive statistics - measures of dispersion

What is the range?

The difference b/w the highest and lowest data items in a data set

Descriptive statistics - measures of dispersion

What is a strength of using range?

Easy to calculate, especially compared to standard deviation

Descriptive statistics - measures of dispersion

What are the weaknesses of using range?

• Extreme scores easily distort the value

• Failed to take into account the distribution of numbers, eg: doesn't show whether most numbers are closely grouped around the mean or spread out evenly

Descriptive statistics - measures of dispersion

what is standard deviation?

• Shows the amount of variation in a data set

• Assesses the spread of data around the mean

Descriptive statistics - measures of dispersion

Strengths of using standard deviation?

• More sensitive than the range includes all values in the calculation

• Provides info about the spread of scores (unlike range)

Descriptive statistics - measures of dispersion

What is a weakness of Standard deviation?

• Bcs includes all values, can be affected by outliers/anomalies + give a misleading answer

• Harder to calculate vs range

Overall - mean

not always representative of data as a whole and should always be considered alongside the SD

Overall - median

has strengths in that is can be used to describe a variety of data sets, including skewed data and non-nominal distributions

Overall - mode

only use mode when appropriate (eg: nominal data sets)

Overall - Range

useful for ordinal data or with highly skewed data or when making a quick calculation

Overall - SD

Best used together w/ the mean to describe interval data which is normally distributed