Statistics - Measures of Location and Spread

Question 1

What is a measure of location?

Answer 1

A measure of location is a single value which describes a position in a data set. If the single value describes the centre of the data, it is called a measure of central tendency.

Question 2

What is the mode?

Answer 2

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

Question 3

What is the median?

Answer 3

The median is the middle value when the data values are put in order.

Question 4

What is the mean?

Answer 4

The mean is the average of the data values.

Question 5

When is the mode used?

Answer 5

This is used when data is qualitative, or quantitative with either a single mode or two modes (bimodal). It is not very informative if each value occurs only once.

Question 6

When is the median used?

Answer 6

This is used for quantitative data. It is usually used when there are extreme values, as they do not affect t.

Question 7

When is the mean used?

Answer 7

This is used for quantitative data and uses all the pieces of data. It therefore gives a true measure of the data. However, it is affected by extreme values.

Question 8

What is the lower and upper quartile?

Answer 8

• The lower quartile is one-quarter of the way through the data set.
• The upper quartile is three-quarters of the way through the data set.

Question 9

How do you find the lower quartile?

Answer 9

To find the lower quartile for discrete data, find 1/4 of n.

• If this is a whole number, the 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 10

How do you find the upper quartile?

Answer 10

To find the upper quartile for discrete data, find 3/4 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 11

What is interpolation?

Answer 11

When the data are presented in a grouped frequency table, you can use a technique called interpolation to estimate the median, quartiles and percentiles. When you use interpolation, you are assuming that the data values are evenly distributed within each class.

Question 12

What is a measure of spread?

Answer 12

A measure of spread is a measure of how spread out the data is.

Question 13

What is the range?

Answer 13

The range is the difference between the largest and smallest values in the data set.

Question 14

What is the interquartile range?

Answer 14

The IQR is the difference between the upper quartile and the lower quartile, Q3-Q1.

Question 15

What are the advantages and disadvantages of the range and the interquartile range?

Answer 15

• The range takes into account all of the data but can be affected by extreme values.
• The interquartile range is not affected by extreme values but only considers the spread of the middle 50% of the data.

Question 16

What is the interpercentile range?

Answer 16

The interpercentile range is the difference between the values for two given percentiles.

Question 17

What is the most common interpercentile range that is used?

Answer 17

The 10th to 90th percentile range is often used since it is not affected by extreme values but still considers 80% of the data in its calculation.

Question 18

What is the variance?

Answer 18

The variance of a dataset is the average of the squares of the deviations of each data point from the mean. The units of the variance are the units of the data squared.

Question 19

What is coding?

Answer 19

Coding is a way of simplifying statistical calculations. Each data value is coded to make a new set of data values which are easier to work with. When data is coded, different statistics change in different ways.