Answer:
Question 1
a) Range
= $2962
b) Variance
= $680557.4954
c) Standard Deviation
= $824.9590871
Question 2
Are there any outliers, and are they likely to have much of an effect on the measures of variation?
Yes, there are outliers present I the given sample data.
These outliers are the larger cost for marriage proposals which are: 1750, 3000
These largest costs are much bigger than the rest of the sample data, and they would likely have much of an effect on the measures of variation
Explanation:
We are given the following sample data in dollars
38, 50, 50, 55, 55, 95, 95, 130, 180, 213, 250, 350, 450, 1750, 3000
Question 1
a) Range
This is the difference between the maximum cost and the minimum cost
The minimum cost = $38
The maximum cost = $3000
Range = $3000 - $38
= $2962
b) Variance
Reading the question, we are given sample data.
Hence, we use the formula for Variance of a sample
= (Mean - x)²/N - 1
Step 1
We find the Mean
Mean = Sum of terms/Number of terms
Number of terms = 15
Mean = 38 + 50 + 50 + 55 + 55 + 95 + 95 + 130 + 180 + 213 + 250 + 350 + 450+ 1750 + 3000/15
= $6761/15
= $450.7333333
Step 2
(x - Mean)²/N - 1
N = 15
= $[(38 - 450.7333333)²+ (50 + 450.7333333)²+( 50 +450.7333333)² + (55 +450.7333333)² + (55 +450.7333333)² + (95 + 450.7333333)²+ (95 +450.7333333)²+ (130 +450.7333333)²+ (180 +450.7333333)² + (213 + 450.7333333)²+ (250 +450.7333333)² + (350 + 450.7333333)² + (450 +450.7333333)²+ (1750 +450.7333333)² + (3000 +450.7333333)²]/15 - 1
=$ (- 412.7333333² + -400.7333333² + -400.7333333² + -395.7333333² + -395.7333333² + -355.7333333² + -355.7333333² + -320.7333333² + -270.7333333² + -237.7333333² + -200.7333333² + -100.7333333² + -0.7333333333² + 1299.266667² + 2549.266667²)/15 - 1
= $( 170348.8044+ 160587.2044, 160587.2044+ 156604.8711, 156604.8711+ 126546.2044, 126546.2044+ 102869.8711, 73296.53776+ 56517.13776, 40293.8711+ 10147.20444+ 0.5377777777+ 1688093.872, 6498760.539)/14
= $9527804.935/14
Variance = $680557.4954
c) Standard deviation = √Variance
Standard deviation = √$680557.4954
= $824.9590871
Question 2
Are there any outliers, and are they likely to have much of an effect on the measures of variation?
Yes, there are outliers present in the given sample data.
These outliers are the largest cost for marriage proposals which are: $1750 and $3000
These largest costs are much bigger than the rest of the sample data, and they would likely have much of an effect on the measures of variation.