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?7 50 50 55 65 75 80 110 190 211 255 350 500 2000 3000 The range of the sample data is _____

Answer 1

`Range = Max -Min= 3000-7 = 2993 dollars`

`s^2 = (\sum_(i=1)^n (X_i -\bar X)^2)/(n-1)`

And after replace we got
`s^2=734983.55 dollars^2`

`s =√(734983.55)=857.312 dollas`

For this case we can consider as an outilers values that are very far away from the others. And for example 2000 and 3000 could be considered outliers since are too high values compared to the remain and the same for 7 since is a value too low compared with the rest.

Explanation:

The data given : 7 50 50 55 65 75 80 110 190 211 255 350 500 2000 3000

The range is defined as:

`Range = Max -Min= 3000-7 = 2993 dollars`

In order to find the variance and deviation we need to find first the mean given by:

`\bar X = (\sum_(i=1)^n X_i)/(n)= (7+50+50+55+65+75+80+110+190+211+255+350+500+2000+3000)/(15)=466.53 dollars`

Now we can calculate the sample variance with the following formula:

`s^2 = (\sum_(i=1)^n (X_i -\bar X)^2)/(n-1)`

And after replace we got
`s^2=734983.55 dollars^2`

And the standard deviation for the sample would be just the square root of the sample variance:

`s =√(734983.55)=857.312 dollas`

For this case we can consider as an outilers values that are very far away from the others. And for example 2000 and 3000 could be considered outliers since are too high values compared to the remain and the same for 7 since is a value too low compared with the rest.