Recognising the shape of data

Symmetry

Data may be described as symmetrical or asymmetrical. 

The normal distribution is the most common example of symmetrical data. The normal distribution looks like this:

The '0' point right in the middle of the distribution represents the mean, the median and the mode- all these measures of central tendency are equal. If we use that '0' line as our axis of symmetry, do you notice how the left hand side is a perfect reflection of the right hand side? That means it's symmetrical.

If your data is asymmetrical (ie. it isn't symmetrical), it may be described as skewed.

 

Skew

Positive skew

A positive skew means that the majority of the scores are low and the long tail is on the positive side of the peak of the graph. It is also sometimes called a right skew. This means the mean is greater than the median, which is greater than the mode.

MODE < MEDIAN < MEAN

A positively skewed graph looks something like this.

Notice how most of the scores are in the lower half of the graph?

 

Negative Skew

A negative skew means that the majority of the scores are high and the long tail is on the negative side of the peak. It is also sometimes called a left skew. This means the mode is greater than the median, which is greater than the mean.

MEAN < MEDIAN < MODE

A negatively skewed graph looks something like this.

Notice how most of the scores are in the higher half of the graph?

 

Worked Examples

Question 1

QUESTION 2

QUESTION 3