Averages, outliers, skewness & histograms

Question 1

What are the three types of skew?

Answer 1

Symmetrical, positive or negative skew

Question 2

Define ‘positive skew’

Answer 2

The median is closer to the lower quartile, with the values above the median spread out more

Question 3

Define ‘negative skew’

Answer 3

The median is closer to the upper quartile, with the values below the median spread out more

Question 4

Define ‘symmetrical distribution’

Answer 4

The median is exactly half way between the lower and upper quartiles

Question 5

What type of skewness is this graph?

Answer 5

Positive skew

Question 6

What type of skewness is this graph?

Answer 6

Negative skew

Question 7

What type of skewness is this graph?

Answer 7

Symmetrical distribution/skew

Question 8

What is the formula for frequency density?

Answer 8

frequency / class width

Question 9

How do you identify outliers?

Answer 9

Upper bound: Q₁ - (IQR x 1.5)

Lower bound: Q₃ + (IQR x 1.5)

Question 10

What are the three main types of average?

Answer 10

Mode, median and mode

Question 11

How do you work out the mode?

Answer 11

The most common value(s) in the data set, there can be no mode

Question 12

How do you work out the median?

Answer 12

The middle most value,

can be calculated with n+1 / 2 or n / 2

Question 13

When do you use n / 2 for the median?

Answer 13

For a cumulative frequency curve

Question 14

Which average is best if you are considering the demand for items of clothing in different sizes, or when data is non-numeric?

Answer 14

Mode

Question 15

Which average is best if you are considering the skew of data?

Answer 15

Median

Question 16

Which average is best if you are wanting to take into account all of the data, or to allow calculations of standard deviation?

Answer 16

Mean