Looking at data

1
Looking at data

• Describing distributions with numbers

2
Numerical descriptions

• Measures of central tendency
• Wheres the middle of the data?
• Most popular mean and median.
• Measures of dispersion
• How much variation is there in the data?
• Most popular variance, standard deviation,
  range, and inter-quartile range (IQR).

3
Mean

• Sum data points and divide by number of data
  points
• The mean is the arithmetic average.
• Provides balance point of data
• Easily influenced by outliers
• Easy to calculate and interpret for audiences

4
Median

• Sort the data points the median is middle data
  point.
• Interpolate between middle 2 data points if
  sample size is even.
• Not very susceptible to outliers
• In other words, the median is a resistant
  measure.
• Not as easy to interpret for audiences, often
  less useful mathematically

5
Symmetry

• In this example, mean and median differ by lt
  1/100
• When mean median, dist. is symmetric
• Think left half is mirror image of right -gt
  symmetric

6
Right skew

• Mean is 3.07, median is 2.76
• Since mean gt median, population has a right skew
• Think tail extends to the right -gt right skew

7
Left skew

• Mean is 0.6625, median is 0.673
• Since mean lt median, population has a left skew
• Think tail extends to the left -gt left skew