Measures of Dispersion

Question 1

For DISCRETE data, how do we find the:

1. Lower Quartile?
2. Upper Quartile?
3. Median?

Answer 1

1. LQ = (n+1)/4
2. UQ = 3(n+1)/4
3. Median = (n+1)/2

Question 2

For CONTINUOUS data, how do we find the:

1. Lower Quartile?
2. Upper Quartile?
3. Median?

Answer 2

1. LQ = n/4
2. UQ = 3n/4
3. Median = n/2

Question 3

What are percentiles? Deciles? Interpercentile range? Interdecile range?

Answer 3

1. Percentiles - data is divided into 100 equal parts
2. Deciles - data is divided into 10 equal parts
3. IPR - difference between two percentiles
4. IDR - difference between two deciles

Question 4

What is the standard deviation?

Answer 4

A measure of how much all the values deviate from the mean or how spread out the values are - the bigger the s.d., the wider the spread of numbers

Question 5

How do we calculate the standard deviation for DISCRETE data?

Answer 5

Standard deviation =√ Σx^2/n - (Σx/n)^2

i.e the square root of : sum of x squared over n minus sum of x over n squared

Question 6

How do we calculate the standard deviation for GROUPED data?

Answer 6

Standard deviation = √ Σfx^2/Σf - (Σfx/Σf)^2

i.e the square root of : the sum of frequency times x^2 divided by total frequency minus (the sum of frequency times x divided by total frequency) squared