Measures of central tendency

Question 1

What is a nominal measurement?

Answer 1

• Things that can’t be expressed as meaningful numbers
• Things that we can name
• More qualitative
• Also called categorical data

Question 2

What is a numerical measurement?

Answer 2

• Things that can be expressed in meaningful numbers/scores
• Can be quantified

Question 3

What is interval data?

Answer 3

• Equal intervals between each number on scale
• E.g., temp
• 0 does not mean absence

Question 4

What is Ratio data?

Answer 4

• Equal intervals between each number on scale, and there is a true 0
• True 0 = indicates absence of the thing we are measuring
• Therefore, we can measure the ratio of things
• E.g., a neuron doesn’t fire

Question 4

What is true zero?

Answer 4

Indicates the absence of the thing we are measuring. For example a neutron doesn’t fire

Question 5

What is a frequency table?

Answer 5

A count of how many times a certain response occurs in a data set
For larger data sets, can categorise x
X = variable name
f = frequency of each value
∑= summation
n= sample size

Question 6

What is ordinal data?

Answer 6

• Numerically measured and ranked, but each position does not necessarily have the same meaning
• E.g., finishing positions in a race – can rank from 1st to 20th, but this tells us nothing about the distances between each rank

Question 7

What is a Histogram?

Answer 7

• Like a grouped frequency table in a graph
• Usually 10 or fewer groups to make the data easier to understand
• Histograms allow us to see issues in our data
• An example of an issue is whether the data is skewed
• when peak of data is on the left with a long tail on the right, the data is positively skewed
• when peak of data is on the right with a long tail on the right the data is negatively skewed

Question 8

Evaluate using the Mean as a measure of central tendency

Answer 8

+ finds best value to represent whole data set
- very heavily affected by outliers

Question 9

Evaluate the use of the mode as a measure of central tendency

Answer 9

+ can be found even for nominal data
- can be more than one mode, or even no mode at all

Question 10

Evaluate the use of the median as a measure of central tendency

Answer 10

+ not affected by outliers
- when there is an even number of data points, we have to take the mean of the two middle items, so the resulting median may not actually be part of the data set

Question 11

When would you use the mean

Answer 11

mean is generally the most preferred measure

useful when there are no significant outliers that will skew the results

Question 12

When would you use the median?

Answer 12

generally used when there are outliers, or the distribution is heavily skewed

may be better for ordinal data

Question 13

when would you use the mode?

Answer 13

generally the best for nominal data, when we can’t calculate the mean or median