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Step2247 [10]
3 years ago
15

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
Mathematics
1 answer:
NNADVOKAT [17]3 years ago
8 0

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

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.

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