Data Distributions & The Normal Distribution Flashcards
What are the different types of data distributions?
- Normal (Gaussian)
- Non-normal
- Bimodal
- Positive/Negative skew
- Uniform
Define data distribution
How much data for a particular variable is spread over its range
How can you tell if the distribution is normal on a Histogram?
Usually, there’s a peak on the histogram (shape looks like a hill) which indicates the data is normally distributed
Does sample size affect distribution?
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
What are the 2 types of non-normal distribution of data?
1) Bimodal
2) Skewed
What does skewed non-normal data look like on a histogram?
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)
What does bimodal non-normal data look like on a histogram?
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)
What is the danger of skewed non-normal data?
The mean is distorted by tails (the mean is not exactly in the middle because it gets dragged by extreme values)
How can we overcome the mean that is distorted by tails in skewed non-normal data?
Use the median as a measure of central tendency
What is the danger of bimodal non-normal data?
Mean is not representative (because there are 2 peaks/modes)
What shape is a normal distribution curve?
Bell-shaped
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
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