Data Distributions & The Normal Distribution

Question 1

What are the different types of data distributions?

Answer 1

• Normal (Gaussian)
• Non-normal
• Bimodal
• Positive/Negative skew
• Uniform

Question 2

Define data distribution

Answer 2

How much data for a particular variable is spread over its range

Question 3

How can you tell if the distribution is normal on a Histogram?

Answer 3

Usually, there’s a peak on the histogram (shape looks like a hill) which indicates the data is normally distributed

Question 4

Does sample size affect distribution?

Answer 4

Yes (normal distribution)

Small sample = We don’t have much
data so normal distribution can be difficult to see in a histogram

Large sample = Normality will emerge

Question 5

What are the 2 types of non-normal distribution of data?

Answer 5

1) Bimodal
2) Skewed

Question 6

What does skewed non-normal data look like on a histogram?

Answer 6

When data on a histogram starts off as a peak and is followed by a tail (positively skewed)

When data on a histogram starts off as a tail and is followed by a peak (negatively skewed)

Question 7

What does bimodal non-normal data look like on a histogram?

Answer 7

When data on a histogram starts off as a peak, dips and then goes back to a peak again (opposite of a normal distribution/ ‘U’ shape)

Question 8

What is the danger of skewed non-normal data?

Answer 8

The mean is distorted by tails (the mean is not exactly in the middle because it gets dragged by extreme values)

Question 9

How can we overcome the mean that is distorted by tails in skewed non-normal data?

Answer 9

Use the median as a measure of central tendency

Question 10

What is the danger of bimodal non-normal data?

Answer 10

Mean is not representative (because there are 2 peaks/modes)

Question 11

What shape is a normal distribution curve?

Answer 11

Bell-shaped

Question 12

Assume that the ratio of 2nd digit length to 4th digit length (i.e. 2D/4D) in the population follows a normal distribution with mean 0.965 and standard deviation 0.025, i.e. follows N(0.965, 0.025).

What is the 2D/4D ratio of someone who is 3 standard deviations above the mean?

a.	0.975

b.	1.0

c.	1.025

d.	1.04

Answer 12

mu - 3 x sigma = 3 s.d.’s below the mean
mu + 3 x sigma = 3 s.d.’d above the mean

0.965 + 3 x 0.025 = 1.04
(mean) + 3 x (SD) = ratio

Answer = D