Question

Instructions and Grading Question 1. (3 points total) Below is a histogram of the salaries of the New York Yankees baseball team in 2011. Use the histogram to answer the following questions. Provided are some summary statistics of the data set. Standard Median Q1 Deviation Minimum Max Mean 03 $414,000 $32,000,000 $6,756,301 $8,468,058 $2,100,000 $559,625 $10,000,000 (1 point) Describe the histogram, commenting on the shape, center and overall spread. (Do your best at estimating what the center would be) a) Salaries of New York Yankees 2011 0 S00 500020300 (2 points) What proportion of players make more than $25,000,000? Show work. (note that 25,000,000 = 250). There is a total of 30 players. b) USD (n $100,000) 100,000

Answer 1

Solution1a:

mean=6756301

median=2100000

mean>median

distribution is positively skewed.

right skewed.

use median to describe the center with the lower and upper quartiles to describe the spread.

median=2100000

Q1=559625

Q3=10000000

we can see there is an outlier

SOlution1b:

P(X>25000000)

P(Z>25000000-6756301/8468058)

P(Z>18243699/8468058

P(Z> 2.154414)

=1-P(Z<2.154)

=1-0.9842

=0.0158

total=30

proportion=probability*sampleszie

=0.0158*30

= 0.474

=0.5

ANSWER:0.5

Solution2a:

IQR=Q3-Q1=10000000-559625=9440375

Solution2b:

lower limit=Q1-1.5IQR=559625-1.5*9440375=-13600938

upper limit=Q3+1.5IQR=10000000+1.5*9440375=24160563