Question

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

Answer 1

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

38, 50, 50, 55, 55, 95, 95, 130, 180, 213, 250, 350, 450, 1750, 3000

The range :

(maximum - minimum) = (3000 - 38) = 2962

Variance :

Σ(x - mean)² / (n-1)

Where n = number of observations

Mean = (38+50+50+55+55+95+95+130+180+213+250+350+450+1750+3000) = 6761 / 15 = $450.73

Σ(x - mean)² = 9527804.9333334

N - 1 = 15 - 1 = 14

Hence,

Variance = Σ(x - mean)² / (n-1)

Variance = 9527804.9333334 / 14

Variance = $680557.50

Standard deviation = √variance

Standard deviation = √680557.50

Standard deviation = $824.96

CHECK IF OUTLIERS EXIST:

Using the outlier formula:

Lower outlier = Q1 - (1.5 × IQR)

Upper outlier = Q3 + (1.5 × IQR)

Q1 = 55 ; Q3 = 350 ; IQR = 295

Lower outlier = 55 - (1.5 × 295) = - 387.5

Upper outlier = 350 + (1.5 × 295) = 792.5

Remove values below the lower outlier value and values above the upper outlier value.

Hence outliers in the data are : 1750 and 3000

To save computation time :

We can recalculate our statistical measure by leaving out the outliers using online, excel or calculator functions :

Data without outlier :

38, 50, 50, 55, 55, 95, 95, 130, 180, 213, 250, 350, 450

Range = (450 - 38) = 412

Variance = Σ(x - mean)² / (n-1)

Variance = 201626.77 / 12

Variance = $16,802.23

Standard deviation:

√variance

√16,802.23

= $129.62341

According to the results obtained the presence of outliers has a great effect on the outcome the result.