Module 3 Assignment

Question A

The following are two sets of data - each consist of 7 observations (n=7).
Set#1:  10, 2, 3, 2, 4, 2, 5
Set#2:  20, 12, 13, 12, 14, 12, 15

  • A1. For each set, compute the mean, medium, and mode under Central Tendency
  • A2. For each set, compute the range, interquartile, variance, and standard deviation under Variation
  • A3. Compare your results between set#1 vs. set #2 by discussing the differences between the two sets.
A1: Central Tendency

Set 1:

  • Mean:4
  • Median: 3
  • Mode: 2 

  Set 2:

  • Mean: 14
  • Median: 13
  • Mode: 12 

A2: Variation

Set 1:

  • Range: 8
  • Quartiles 
    • Q1: 2
    • Q3: 5
  •  Interquartile Range: 3
  • Variance: 8.67
  • Standard Deviation: 2.94

Set 2:

  • Range: 8
  • Quartiles
    • Q1: 12
    • Q3: 15
  •  Interquartile Range: 3
  • Variance: 8.67
  • Standard Deviation: 2.94

A3: Comparison

By analyzing and comparing both datasets, I noticed that they both have the same spread. This is conveyed by the fact that they have the same values for the range, interquartile range, variance, and standard deviation.

While this is true, the two sets contrast each other immensely with one thing, the fact that set #2 is a shifted version of set #1. All values in set#2 are 10 units larger than set#1. Therefore, set#2 ends up having larger values for the mean, median, and mode.

In conclusion, this demonstrates that the measures of central tendency can differ between the two sets, but the measures of variation remains the same. 

 

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