Using data

Numerical - measures of central tendency and dispersion

Bar charts

Pictorial - charts and graphs

Line graphs

Mean

Standard deviation

Mode

Median

Range

Inter-quartile range

The arithmetic average that is calculated through adding all of the values and then dividing by how many there are.

The middle number after all numbers have been ordered

The most frequent number in a set

• Contributed to by all values

• Preferred when data is skewed

• Useful in statistics

• Used within continuous data

• Preferred when data is normally distributed

• Easiest to understand and calculate

• More difficult to understand

• Time consuming

• Affected by extreme values

• Not appropriate with ordinal and nominal level data

• Might not be an actual value in the set

The sum of all values divided by the number of values

The middle number after all numbers have been ordered

• Easier to understand

• Easiest to understand and calculate

• Unaffected by extreme values

• Used with ordinal and continuous data

• An actual value

• Preferred when data is skewed

• Might not be an actual value in the set

• Time consuming

• Not appropriate with ordinal and nominal level data

The middle number after all numbers have been ordered

The most frequent number in a set

• Easiest to understand and calculate

• Used with categorical data

• An actual value

• Preferred when data is skewed

• Unaffected by extreme values

• Affected by extreme values

• Sometimes there is more than one

• More difficult to understand

Mean

Range

Mode

Interquartile range

Standard deviation

Median

How much on average each score deviates from the mean score.

The difference between the largest and the smallest.

• Easy to understand

• Related to the actual values in the set

• Useful in statistics

• Usual used with ordinal and continuous data

• More difficult to understand

• Affected by extreme values

The difference between the upper quartile (75% data point) and the lower quartile (25% data point).

How much on average each score deviates from the mean score.

• Related to the actual values in the set

• Useful in statistics

• Used with continuous data

• Usually used with ordinal and continuous data

• Unaffected by extreme values

• More difficult to understand

• Unlikely to be a value in the set

How much on average each score deviates from the mean score.

The difference between the upper quartile (75% data point) and the lower quartile (25% data point).

• Uses all the values in the set

• Easy to understand

• Useful in statistics

• Used with continuous data

• Usually used with ordinal and continuous data

• Affected by extreme values

• More difficult to understand

• Unlikely to be a value in the set

This is normal because the mean, median and mode lies in the same place, the mean is the preferred method.

The mean is dragged in the direction of the skew so the median is the preferred measure (an easy test – ceiling effect).

The mean is dragged in the direction of the skew so the median is the preferred measure (an easy test – ceiling effect).

Left

Right

The mean is dragged in the direction of the skew so the median is the preferred measure (an easy test – ceiling effect).

Left

Right

Median

Mode

Mean

Mode

Median

They are helpful for indicating whether a distribution is skewed and if there any unusual observations (outliers) in the data set.

They are useful when large numbers of observations are involved or comparing two or more data sets.

Bar chart

Line graph

Scatter diagram

Pie chart

Nominal data

Continuous data

Ordinal data

Ratio data

Categorical data

Interval data

When quantities that are ordered y criteria such as positions in a rate. However it does not allow you to state whether the intervals between each value are equal.

categorically discrete data such as the name of your school or the car you drive.

This is like like ordinal data except the intervals between each value is equally split, such as the time of day on a clock.

like ordinal data except the intervals between each value is equally split, such as the time of day on a clock.

interval data with a natural zero point (ruler in cm).

When quantities that are ordered y criteria such as positions in a rate. However it does not allow you to state whether the intervals between each value are equal.

The median could be a measure of central tendency for this.

The median could be a measure of central tendency for this.

this is like ordinal data except the intervals between each value is equally split, such as the time of day on a clock.

this is like ordinal data except the intervals between each value is equally split, such as the time of day on a clock.

interval data with a natural zero point (ruler in cm).

data which is divided into groups (types of animals). This data is nominal and discrete.

The mode would be the measure of central tendency as it cannot be used with arithmetic.

Representations could include a bar chart with gaps between the bars (grouped discrete data)

data restricted to a limited set of discrete values (shoes size and money)

data which can take any value within a range (height). The mean could be a measure of central tendency, this is because it would give you the arithmetic average for the large range of data which can then be used in statistics.

The median could be used if the data was skewed because this would be more representative of the data.

Representations could include a line graph or a histogram (grouped continuous)

data restricted to a limited set of discrete values (shoes size and money)

data which is divided into groups (types of animals). This data is nominal and discrete. The mode would be the measure of central tendency as it cannot be used with arithmetic.

Continuous

Standard deviation

Ordinal data

Skewed data

Categorical data

Ordinal data

Nominal data