1The histogram shows the sizes of vineyards measured in acre

1.)The histogram shows the sizes of vineyards (measured in acres) in a sample taken from all vineyards in Wine Country, CA. Use the histogram to answer the following questions.

a.            How many vineyards are between 120 and 210 acres in size?

b.            Give the relative frequency of the vineyards that are less than 150 acres.

c.             How would you describe the shape of this distribution? Choose all that apply:

                symmetric           unimodal            bimodal                uniform                              skewed right       skewed left     

d.            Which class interval would contain the median vineyard size? Select one.

0 ? 30   

30 - 60

60 - 90  

90 ? 120

120 - 150

150 - 180

180 - 210

210 - 240

240 ? 270

270 - 300

e.            Considering the distribution of vineyard sizes shown in the graph, how do you expect the mean and median will compare? Choose one:

o             The mean is smaller than the median.

o             The mean and median are approximately equal.

o             The mean is larger than the median.

f.             Based on the histogram, are there any suspected outliers? If so, describe the size of the vineyard(s) that is an outlier.

Solution

a)3+4+9=16

b) in total there are 1+2+3+4+9+10+14+2=45

less than 0 and between 30 and 90, relative frequency 0/45=0

between 0 and 30, 1/45

between 90 and 120, 2/45

between 120 and 150, 3/45

c) unimodal

skewed left

d)since there are 45, the median is where 45/2=22.5 is

so we have cumulative frequency 1+2+3+4=10 didn\'t reach

10+9=19 still didn\'t reach

19+14=33 it passed 22.5

so 22.5 is between 240 and 270

e) the mean is smaller than the median

that happens when there are few unusual smaller values, which makes the mean smaller

f) yes, between 0 and 30 vineyard size there is an unusual smaller size out of the bulk of other sizes