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.

an advantage of the standard deviation is that it increases as the dispersion of the data increases. e. the interquartile range is preferred when the data are not skewed or no have outliers. an advantage of the standard deviation is that it uses all the observations in its computation.

answer: (yeees, you need a poet.)

//blooming serenity//

beautiful in the morning

mysterious at night

wonderous nature souring

with all it's mystical might

the flower that blooms

to the fox that looms

nocturnal creatures

with various features

a blooming flower soon in sight

as a new little hatchling fears to take flight  

afraid to leave it's calming nest,

but dear little bird, mother knows best

as sure as there are stars in the sky,

life is not about who, where what, when or why-

it's the journey that follows

adventures we swallow

of   nature's deep wonders,

natural disasters and storm's thunders.

blooming serenity

life and nature, truly is heavenly.

-kerstien lehman

step-by-step explanation: