Module 3- Descriptive Statistics

2/2/25

It is week 3, and this week we are beginning to use R for descriptive statistics. The first question is pasted below: 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
1. For each set, compute the mean, median, and mode under Central Tendency

Set 1:                         

Mean- 4

Median- 3

Mode- 2

Set 2:

Mean- 14

Median- 3

Mode- 2

2. For each set, compute the range, interquartile, variance, standard deviation under Variation

Set 1:

Range- (2, 10)

Interquartile- 2.5

Variance- 8.33

Standard Deviation- 2.89

Set 2:

Range- (12, 20)

Interquartile- 2.5 

Variance- 8.33

Standard Deviation- 2.89

3. Compare your results between set#1 vs. set #2 by discussing the differences between the two sets

As seen by the data above, Set#1 has a higher Coefficient of Variation (CV) of 72.17%, showing greater relative variability around its mean of 4. The data in Set#1 is more spread out, with values ranging from 2 to 10. In contrast, Set#2 has a much lower CV of 20.62%, suggesting that its values are more concentrated around the mean of 14, with a range of 12 to 20. Although both sets have similar interquartile ranges (2.5), Set#2 shows less variability and more consistency. Set#1 has a median of 3, while Set#2 has a higher median of 13, indicating a central tendency shift toward higher values in Set#2. Also, Set#1’s mode is 2, whereas Set#2’s mode is 12. The variance and standard deviation values are the same for both sets, at 8.33 and 2.89, respectively, but again Set#2’s lower CV highlights its more consistent data distribution.