Remediation 6.1 CFA Comparing Statistical Measures

Skewed Left or Right

• When a distribution is skewed left the mean is less than the median

• When a distribution is skewed right the mean will be more than the median.

Bell or Symmetrical Distributions

• Symmetrical distributions of data can also be called normal or bell shaped.

• Since their distribution is fairly normal, the mean and the median will be close to the same.

Multiple Choice

Which of the following best describes the shape of the distribution?

• SKEWED LEFT
• SKEWED RIGHT
• UNIFORM
• SYMMETRICAL

Multiple Choice

Describe the shape of the distribution.

• symmetric

• skewed left

• skewed right

Multiple Choice

Describe the shape of the distribution.

• symmetric

• skewed left

• skewed right

Multiple Choice

How is the graph distributed?

• Normally

• Skewed to the Left

• Skewed to the Right

• Uniform

Multiple Choice

How is the graph distributed?

• Normally

• Skewed to the Left

• Skewed to the Right

• Uniform

Find the median in a nonsymmetrical distribution. In a bell shaped or symmetrical the mean and median are the same thing.

​Center

Center and Spread of Data

To find the spread find the "Range" by subtracting your biggest and smallest numbers.

Spread

​Outlier

• ​An outlier is a value far from the rest of the data in a set

• ​Removing or adding an outlier will affect the range

• Removing or adding an outlier will not (most of the time) affect the median

• Removing or adding an outlier will affect the mean​

Multiple Choice

What is the median?

• The number in the middle

• The difference between the highest and lowest values

• The number that occurs the most

• The average

Multiple Choice

What does the mean measure of central tendency signify and when is it most appropriate to use?

• The mean represents the highest value in the data and is most appropriate to use when the data is skewed to the right.

• The mean represents the lowest value in the data and is most appropriate to use when the data is skewed to the left.

• The mean represents the central value of the data and is most appropriate to use when the data is normally distributed and there are no extreme outliers.

• The mean represents the most frequently occurring value in the data and is most appropriate to use when the data has a wide range of values.

Multiple Choice

In what scenario would you choose to use the mean as the measure of central tendency over the median and mode?

• When the data is skewed to the right

• When the data is normally distributed and there are no extreme outliers.

• When the data has multiple modes

• When the data has extreme outliers

Multiple Choice

When working with skewed data, which measure of central tendency would you rely on the most and why?

• Median

• Mean because it is the most commonly used measure of central tendency

• Range because it shows the spread of the data

• Mode because it represents the most frequent value in the data

Multiple Choice

Given that the data is symmetric, which pair of measures should be used to represent the data?

• center: median

  spread: standard deviation

• center: mean

  spread: IQR

• center: mean

  spread: standard deviation

• center: median

  spread: IQR

Multiple Choice

Which measure of spread should be used to describe the distribution?

• standard deviation

• interquartile range

• range

• median