Normal and Skewed Distribution

Question 1

Normal and Skewed Distribution

Answer 1

These distributions refer to how the values from a given set of data are dispersed when plotted on graphs.

Variables in real life such as height, weight, shoe size and IQ scores are said to show the normal distribution (bell shaped).

This means most people score near the average value. The further you move away from the average value, the fewer scores you will find.

Question 2

How do we obtain these curves from a given set of data?

Answer 2

Organise data in a frequency table and create a histogram plotting height on the x-axis, and the frequency at which each of the heights occurred on the y-axis.

Question 3

Normal Distribution

Answer 3

The 4 characteristics of a normal distribution are: symmetric, unimodal, and asymptotic, and have an equal mean, median and mode.

A normal distribution is perfectly symmetrical around its centre. That is, the right side of the centre is a mirror image of the left side.

It is also unimodal; there is only one mode, or peak, in a normal distribution.

Normal distributions are continuous and have tails that are asymptotic, which means that they approach but never touch the x-axis (values never reach 0 and extreme scores are theoretically possible).

The centre of a normal distribution is located at its peak, it follows that the mean, median, and mode are all equal.

Question 4

Skewed Distribution

Answer 4

Skewed distribution curves are called skewed when they are not symmetrical at the mean (or median or mode) point. A skew can be positive or negative.

Question 5

Negatively Skewed or Left Skewed Distribution

Answer 5

The majority of the data values fall to the right of the mean at the upper end of the distribution.
Remember: Negatively skewed - the tail is to the left.
The ‘tail’ will be longer where the values of the scores (of either exam tests, memory tests) is the smallest. In such cases, there are higher number of high scores (most people do better than average). For example, an exam that was particularly easy.
Examples: Age at death, number of doughnuts purchased or number of applications completed before getting a job.

Question 6

Positively Skewed or Right Skewed Distribution

Answer 6

The majority of the data values fall to the left of the mean at the lower end of the distribution.
Remember: Positively skewed - the tail is to the right.
The ‘tail’ will be longer where the values of the score (of either exam tests, memory tests) is larger. In such cases, there are higher number of lower scores (most people do worse than average). For example, an exam that was particularly difficult.
Examples: People’s incomes, house prices, number of children in a family.