Question

Here are summary statistics for the sizes (in acres) of a collection of vineyards in the Finger Lakes region of New York State:

Count	36
Mean	46.5
StdDev	47.76
Median	33.5
IQR	36.5
Min	6
Q1	18.5
Q3	55
Max	250

1. Based on the summary statistics, would you describe the distribution as symmetric or skewed. Explain.
2. Are there any outliers? Explain.
3. Write a report on the vineyard sizes in the Finger Lakes Region (i.e., write a few sentences discussing the summary statistics).

Typed answers please.

Answer 1

Solution:

a)Here the median is left of the mean because the median is less than the mean

i.e meadian=33.5< mean= 46.5  

Therefore the distribution is skewed to the right.

b) To find the lower fence:

Now the formula of lower fence is given by

The lower fence = Q1-1.5(IQR)

=18.5-1.5(36.5)

=18.5-54.75

=-36.25 <6

=Minimum value

Now to find the upper fence:

The formula of upper fence is given by

The upper fence = Q3+1.5(IQR)

= 55+1.5(36.5)

= 55+54.75

=109.75

Outlier means any data value is larger than upper fence Q3+1.5(IQR) or smaller than lower fence Q1-1.5(IQR).

Here -36.25 < 6,so -36.25 is an otlier.and 250 should greater than 109.75.Therefore there are ouliers in the data set.

c). The center 50% of vineyards are somewhere in the range of 18.50 and 55 acres.The 36 veniyards are average of 46.50 acres,with sizes extending from 6 acres to  250 acres.