Lesson 2- Data Description

Question 0

Measures of center

Answer 0

• mean: X resistant to outliers
• median: resistant
• mode

Question 1

Quantitative description of data

Answer 1

• center: mean, median, mode

- spread (variability): range, quartiles (IQR), variance, standard deviation

Question 2

Measures of spread

Answer 2

• range (max. - min.)
• quartile (Q1, M, Q3)
• IQR: middle 50%
• outlier criterion: if observation falls 1.5(IQR) below Q1 or above Q3

Question 3

Boxplots

Answer 3

• show right or left-skew
• 5 number summary (min, Q1, M, Q3, max)
• central box spans quartiles
• line in box is median
• conceals outliers

Question 4

Modified boxplot

Answer 4

-outliers plotted individually

Question 5

Standard deviation

Answer 5

s= [ 1/(n-1)*sum(xi -xmean)^2 ] ^ (1/2)

Question 6

Measures of spread 2

Answer 6

• standard deviation
• degrees of freedom: the sum of deviations = 0, the last deviation can be found once we know the other n-1 deviations, only n-1 can vary freely therefore we divide by n-1
• variance = s^2

Question 7

Effect of changing units of measure

Answer 7

• linear transformation, x -> a + bx
  
  • effect of ‘a’: adds a to center and quartiles, but X effect on spread
  • effect of ‘b’: multiplies both center and spread (StD, IQR) by b
• skew, median, mean
  
  • right-skew: mean is greater than median. CFP goes up quickly
  • left-skew: mean is less than median. CFP goes up slowly