DESCRIPTIVE STATISTICS

NUMERICAL MEASURES

• Answers what has happened in the past

• Sample can provide estimates for a population parameter

• Sample statistics - Measures are computed from a sample 

  • Sample statistics - point estimate of corresponding population parameter

• Population parameter - Measures are computed from population 

• ML: Mean

• - average of all data values

  • sum of observations/no. of observations

• ML: Median

• - value in the middle arranged in ASCENDING ORDER

  • Odd numbers - simply get the middle range

  • Even numbers - get the average of the 2 middle values by adding them and divide by 2

    • (19 + 26)/2 = 22.5

• ML: Mode -

• value that occurs with greatest frequency

  • Bimodal - two modes

  • Multimodal - more than two modes

ML: Percentiles

provides interval from the smallest to largest value

• No 0 or 100 percentile ONLY 1 to 99

  • Arrange in ascending order

  • Lp= p100(n + 1)

• ML: Quartiles -

• Specific percentiles

• Q1 = 25th percentile,

• Q2= 50th percentile (median/middle)

• Q3= 75th percentile

Lp= p100(n + 1)

MV: Range

• - difference between largest and smallest data values

  • largest - smallest = range (ascending order)

MV: Interquartile Range -

• difference between first & third quartile

  • Range for middle 50% 

Q3 - Q1 

MV: Variance

- measure of variability utilizing all data

• Based on difference on value of each observation minus the mean

• Average of squared differences between each data value and the mean

MV: Standard Deviation

- positive square root of the variance