Numerical Methods for Summarising Data

Question 1

What measures of central tendency are there?

Answer 1

Mean, median and mode

Question 2

How can we denote the mean?

Answer 2

Using
_
X

or

n

Question 3

What are the quartiles of distribution?

Answer 3

Q1 = n/4 or 25% of the data

Q2 = n/2 or 50% of the data (middle value)

Q3 = 3n/4 or 75% of the data

Question 4

What do deciles represent?

Answer 4

Each decile represents 10% of the data.

D4, for example, represents the 40% value or the 4th value of 10

Question 5

What do percentiles represent?

Answer 5

Different percentages within the data.

P79 represent 79% of the data or the 79th value of 100 values

Question 6

What is the integer rule?

Answer 6

If 1/4n is an integer, then add 1/2 to get Q1.

If 1/4n isn’t an integer, go to the next whole number to find Q1.

Question 7

What do we use to find values (e.g. Q1, P73 etc) for grouped frequency?

Answer 7

The exact value, using interpolation.

No integer rule!

Question 8

If you have gaps between groups in a grouped frequency table, what value do you use when interpolation?

Answer 8

The midpoint between the two groups.

For example:

If the previous group ends at 19 and the next one starts at 20, use 19.5.

Question 9

How do you interpolate?

Answer 9

Min value + (frequency value you use within the group / total frequency in the group x group width)