4.2.3.2 DISTRIBUTIONS

Question 1

what is normal distribution?

Answer 1

a theoretical frequency distribution represented by a normal curve

• data is symmetrically distributed with no skew
• when plotted on a graph, the data follows a bell shape with most values clustering around a central region and tapering off as they go further away from the centre

Question 2

what is a skewed distribution?

Answer 2

• the measure of the asymmetry of a distribution
• its left and right side are not mirror images
• right-skewed distribution = longer on the right side of the peak (positive skew)
• left-skewed distribution = longer on the left side of its peak (negative skew)

Question 3

what are the characteristics of a normal distribution?

Answer 3

• the mean, median and mode are exactly the same
• distribution is symmetric about the mean - half the values fall below the mean and half above the mean
• the distribution can be described by the mean and the standard deviation
  -> the mean is the local parameter while the standard deviation is the scale parameter
  -> it determines where the peak of the curve is centred
  -> increasing the mean moves the curve right, while decreasing it moves the curve left
  -> the standard deviation stretches or squeezes the curve
  -> a small standard deviation = narrow curve
  -> large standard deviation = wide curve

Question 4

what is the characteristic of a skewed distribution?

Answer 4

not symmetric - one tail is longer than the other