DS 2.01 Measures of Central Tendency Quiz Review

Which wombat do you most relate to at this moment?

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What is the mean of a data set?

• The sum of all the data points divided by the number of data points

• The middle number of a dataset

• The most common value of a dataset

• A number that represents how far a data point is away from what is normal

Answer explanation

The mean of a data set is calculated by summing all the data points and then dividing by the number of data points. This is the correct answer because it accurately represents the statistical concept of 'mean'. The other options describe the median, mode, and a measure of deviation respectively, not the mean.

When should you use the mean as a measure of centrality?

• When you want an outlier to have an effect on your measure of centrality

• When you want a measure that is robust to outliers

• When you want to know the most common value of a dataset

• When you want to measure how not normal something is

Answer explanation

The mean is a measure of central tendency that takes into account each value in the dataset. This makes it sensitive to outliers, which can significantly shift the mean. Therefore, the mean is an appropriate measure of centrality when you want an outlier to influence your measure.

How is the median calculated?

• Sort all values and choose the middle value

• Sum all the data points and divide by the number of data points

• Count up the number of datapoints for each value

• Determine how far from the mean a datapoint can be and still be relatively normal

Answer explanation

The median of a dataset is calculated by sorting all the values in the dataset and then choosing the middle value. If the dataset has an even number of observations, the median is the average of the two middle values. This choice correctly describes the process of calculating the median.

When should you use the median as a measure of centrality?

• When you want an outlier to have an effect on your measure of centrality

• When you want a measure that is robust to outliers

• When you want to know the most common value of a dataset

• When you want to measure how not normal something is

Answer explanation

The median is a measure of central tendency that is not affected by outliers or extreme values in the data set. Therefore, it is used when you want a measure that is robust to outliers. The other options involving the effect of outliers, the most common value, and measuring 'non-normality' do not accurately describe when to use the median.

What does the mode represent?

• The sum of all the data points divided by the number of data points

• The middle number of a dataset

• The most common value of a dataset

• A number that represents how far a data point is away from what is normal

Answer explanation

The mode is a statistical term that represents the most common value in a dataset. It's the value that appears most frequently. The other options described mean, median and standard deviation, which are different aspects of statistical analysis.

When should you use the mode?

• When you want an outlier to have an effect on your measure of centrality

• When you want a measure that is robust to outliers

• When you want to know the most common value of a dataset

• When you want to measure how not normal something is

Answer explanation

The mode is used when you want to identify the most common value in a dataset. Unlike mean or median, the mode is not affected by outliers or skewed data. It simply represents the value that occurs most frequently in the dataset.

What does the standard deviation measure?

• The sum of all the data points divided by the number of data points

• The middle number of a dataset

• The most common value of a dataset

• How not normal something is

Answer explanation

The standard deviation is a measure of how spread out numbers are from their average value. When something is not normal, it means it deviates from what is expected or standard. Therefore, the correct answer to this question is 'How not normal something is', which refers to the variability or dispersion of a dataset.

How is the standard deviation calculated?

• Sort all values and choose the middle value

• Sum all the data points and divide by the number of data points

• Count up the number of datapoints for each value

• Determine how far from the mean a datapoint can be and still be relatively normal

Answer explanation

The standard deviation is a measure that quantifies the amount of dispersion or variation in a set of values. It is calculated by determining how far each datapoint is from the mean. A low standard deviation indicates that the datapoints tend to be close to the mean, while a higher standard deviation indicates that the datapoints are spread out over a wider range.

When should you use the standard deviation?

• When you want an outlier to have an effect on your measure of centrality

• When you want a measure that is robust to outliers

• When you want to know the most common value of a dataset

• When you want to measure how not normal something is

Answer explanation

The standard deviation is used to measure how dispersed the values are in a data set. If something is 'not normal', it means there is a large amount of variation or dispersion in the data set. Therefore, we would use standard deviation in this situation to quantify the amount of variation or dispersion.