Download Section 2.4 Working with Summary Stats

Section 2.4 Working With Summary Statistics
Statistics
P26.) A community in Nevada has 9751 households, with a median house price of
$320,000 and a mean price of $392,059.
a.) Why is the mean larger than the median?
b.) The property tax rate is about 1.15%. What total amount of taxes will be
assessed on these houses?
c.) What is the average amount of taxes per house?
P28.) The mean height of a class of 15 children is 48 inches, the median is 45
inches, the standard deviation is 2.4 inches, and the interquartile range is 3
inches. Find the mean, standard deviation, median, and interquartile range if
a.) you convert each height to feet. (there are 12 inches in 1 foot)
b.) each child grows 2 inches.
c.) each child grows 4 inches and you convert the heights to feet.
P30.) The histogram and boxplot in Display 2.70 and the summary statistics in
Display 2.71 show the record low temperatures for the 50 states.
a.) Hawaii has a lowest recorded temperature of 120F. The boxplot shows
Hawaii as an outlier. Verify that this is justified.
b.) Suppose you exclude Hawaii from the data set. Copy the table in
Display 2.71, substituting the value (or your best estimate if you do not
have enough information to compute the value) of each summary
statistic with Hawaii excluded.
Count
Mean
Median
StdDev
Min
Max
Range
Lower 25 %tile
Upper 75 %tile
P31.) Estimate the quartiles and the median of the SAT I critical reading scores in
Display 2.69 on page 78, and then use these values to draw a boxplot of the
distribution.
200
300
400
500
600
700
What is the IQR?
E49.) The histogram in Display 2.72 (page 81) shows record high temperatures for
the 50 states.
a.) Suppose each temperature is converted from degrees Fahrenheit, F, to
5
degrees Celsius, C, using the formula C   F  32  . If you make a
9
histogram of the temperature in degrees Celsius, how will it differ
from the one in Display 2.72?
800
b.) The summary statistics in Display 2.73 are for record high temperatures
in degrees Fahrenheit. Make a similar table for the temperatures in
degrees Celsius.
N
Mean
Median
StDev
Min
Max
Q1
Q3
c.) Are there any outliers in the data?
E53.) The cumulative relative frequency plot in Display 2.74 (page 81) shows the
amount of change carried by a group of 200 students. For example, about
80% of the students had $0.75 or less.
a.) From this plot, estimate the median amount of change.
b.) Estimate the quartiles and the interquartile range.
c.) Is the original set of amounts of change skewed right, skewed left, or
symmetric?
d.) Does the data set look as if it should be modeled by a normal
distribution? Explain.
E54.) Use Display 2.74 to make a boxplot of the amounts of change carried by the
students.
0
195
130
65
Amount of Change (cents)
260
E57.) The cumulative relative frequency plot in Display 2.76 gives the ages of
CEOs (Chief Executive Officers) of the 500 largest U.S. companies. Does
A, B, or C give its median and quartiles?
A. Q1 51; median 56; Q3 60
B. Q1 50; median 60; Q3 70
C. Q1 25; median 50; Q3 75
E58.) Refer to the distribution of ages in E57. Can you give the median and
quartiles of the distribution of ages in months instead of years?
If so, do it. If not, explain why not.