Statistics 1.2 - Measures of location and spread

Question 1

What is a measure of location?

Answer 1

A single value which describes a position in a data set.

Question 2

What is a measure of central tendency?

Answer 2

Where the measure of location describes the centre of the data.

Question 3

What is the mode?

Answer 3

The mode or modal class is the value or class that occurs most often.

Question 4

What us the median?

Answer 4

The median (Q₂) is the middle value when the data values are arranged in order.

Question 5

What is the mean?

Answer 5

The mean is an average calculated using the formula;
x̄=Σx/n
and for data given in a frequency table;
x̄=Σxf/x̄=Σf
Where x̄ is the mean, Σx is the sum of the data values, n is the number of data values, Σxf is the sum of the products of the data values and their frequencies and Σf is the sum of the frequencies.

Question 6

What are quartiles and percentiles?

Answer 6

Measures of locations that represent different proportions of the data set.

Question 7

What is the lower quartile?

Answer 7

The lower quartile (Q₁) is a measure of location that is one-quarter of the way through the data set. For discrete data, its data point can be found by dividing n by 4, if this is a whole number, the data lower quartile is halfway between this data point and the one above. If it is not a whole number, round up and pick this data point.

Question 8

What is the upper quartile?

Answer 8

The upper quartile (Q₃) is a measure location that is three-quarters of the way through the data set. For discrete data, its data point can be found by finding ¾ of n. If this is a whole number, the upper quartile is halfway between this data point and the one above. If it is not a whole number round up and pick this data point.

Question 9

How are the median and quartiles calculated for a grouped frequency table?

Answer 9

The data values are assumed to be evenly distributed within each class, so interpolation is used to calculate.