2.5 - 2.7 Measures of Center and Variability

Question 1

Define mean. Provided on calculation sheet.
List the properties of the mean.

Answer 1

aka average; the sum of all observations divided by the number of observations
*balancing point of the distribution or dot plot
*usually not an observed value
*NOT resistant to outliers

Question 2

Define outlier.

Answer 2

an observation that is unusually large or small compared with the bulk of the data

Question 3

Define resistance.

Answer 3

when the outliers in a numerical summary have little to no influence on its value

Question 4

Define median.
List the properties of the median.

Answer 4

the middle of the observations when they are put in order; take the avg of the two middle numbers if the sample has an even number of observation
*splits the data in half
*is one of the observations if there is an odd number
*resistant to outliers
*for a skewed distribution, the mean is pulled farther than the median in the direction of the longer tail

Question 5

When the distribution is close to symmetric with no outliers, is mean or median preferred?

Answer 5

mean - NOT resistant to outliers

Question 6

When the distribution is highly skewed, is mean or median preferred?

Answer 6

median - resistant to outliers

Question 7

Define mode.
List the properties of the mode.

Answer 7

the value that occurs most frequently
there can be multiple modes (unimodal, bimodal)
*the value at which a dot plot has its peak
*always one of the observed values
*resistant to outliers

Question 8

Define range.
List the properties of the range.

Answer 8

the largest observation minus the smallest observation
*distance from the far left dot to the far right dot on a dot plot
*NOT resistant to outliers

Question 9

Define standard deviation. Equation will be given on formula sheet.
List the properties of the standard deviation.
Define deviation. What is the sum of all deviations?

Answer 9

*s, δ; a typical distance or type of average distance of an observation from the mean
- find the mean
- find the deviations
-square each deviation
-add these results up
-divide by n-1 (variance)
-take the squre root (standard deviation)
*properties include:
-the greater the variability, the larger the deviation
-when all observations are the same, the standard deviation is 0
-NOT resistant to outliers
*an observation minus the mean; sum = 0