Listed below are the amounts (dollars) it costs for marriage proposal packages at different baseball stadiums. Find the range, variance, and standard deviation for the given sample data. Include appropriate units in the results. Are there any outliers, and are they likely to have much of an effect on the measures of variation? 38, 50, 50, 55, 55, 95, 95, 130, 180, 213, 250, 350, 450, 1750, 3000

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

Step-by-step 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.

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is symmetric about the line y = 120,000.

step-by-step explanation:

step-by-step explanation: yes