Knewton Alta Chapter 2 test- Descriptive statistics -
part 3 with Questions with 100% Correct Answers
The heights, in inches, of the four members of a barbershop quartet of singers are
listed below.
72,68,67,73
Find the population variance for this data set. Round to one decimal place if necessary.
- Answer Correct answers:6.5
First, we find that the mean is
72+68+67+734=2804=70
Now, we need to take the deviations from the mean and square them:
ValueDeviationDeviation2722468−2467−397339
Since there are exactly 4 members of a barbershop quartet, the 4 measurements
given represent the entire population of the singing group. So we calculate the
population variance.
The population variance is the sum of the squared deviations, divided by the number of
data values( 4).
,4+4+9+9/4=6.5
Based on the z-scores calculated above for Angie and Beth, which swimmer had
the fastest time when compared to her team? - Answer Correct answer:
Beth
Angie has a z-score of −1.25 and Beth's z-score is −2.
Both Angie and Beth have negative z-scores, meaning they both swim in less time
than their team's mean time. In terms of swim times, lower values are faster times, so
Beth has the faster swim time when compared to her team.
Your answer:
Angie
Smaller values correspond to faster swim times - who has the smaller z-score?
Karl and Fredo are basketball players who want to find out how they compare to their
team in points per game. The mean amount of points per game and standard deviations
for their team were calculated. Karl's z-score is 0.9. Fredo's z-score is −0.65.
Which of the following statements are true about how Karl and Fredo compare to
their team in points per game? Select all that apply. - Answer Correct answer:
Karl's average points per game is 0.9 standard deviations greater than his
teammates' average points per game.
Fredo's average points per game is closer to the team's mean than Karl's.
The z-score is the number of standard deviations a data value is from the mean of the
data set. Karl's average points per game is 0.9 standard deviations greater than his
team mean. Fredo's average points per game is 0.65 standard deviations less than his
team mean.
But, since Fredo's z-score is −0.65, the distance from this to the mean is less than 0.9.
since |−0.65|<0.9. So, Fredo's average points per game is closer to the team's mean
than Karl's.
,The following data set provides infomation about the City of Somerville
Assessors Valuation for the fiscal year 2016.
Which statements are true about the pattern of data for the sample standard
deviations of the commercial buildings total assessed land value and total assessed
parcel value, and the residential buildings total assessed land value and total assessed
parcel value? Select all that apply. - Answer Correct answer:
Commercial buildings have a greater standard deviation in both categories
than residential.
The largest difference in standard deviation is from Residential Total Assessed
Land Value to Commercial Total Assessed Parcel Value.
The smallest decrease in standard deviation is from Residential Total Assessed
Parcel Value to Residential Total Assessed Land Value.
Commercial buildings do have a greater standard deviation in both categories than
residential. The standard deviation for Commercial Total Assessed Land Value
(4361842) is not more than two times the standard deviation for Residential Total
Assessed Land Value (97477). The standard deviation for Commercial Total Assessed
Land Value is about 45 times more than the standard deviation for Residential Total
Assessed Land Value. The largest difference in standard deviation is from Residential
Total Assessed Land Value to Commercial Total Assessed Parcel Value. The smallest
decrease in standard deviation is from Residential Total Assessed Parcel Value to
Residential Total Assessed Land Value.
Which of the following frequency tables shows a skewed data set? Select all that apply. -
Answer Correct answer:
ValueFrequency13214515116131723182619152012
ValueFrequency04112223328417576673
Remember that data are left skewed if there is a main concentration of large values with
several much smaller values. Similarly, right skewed data have a main concentration of
small values with several much larger values. We can see that the following is left skewed
because of the concentration of large values with many smaller values:
ValueFrequency13214515116131723182619152012
, And the following is right skewed because of its concentration of small values with
many larger values:
ValueFrequency04112223328417576673
The other frequency tables are more balanced and symmetrical.
The following data set provides information about the City of Somerville
Assessors Valuation for the fiscal year 2016.
For residential buildings, what is the sample standard deviation of the land area?
Round your answer to TWO decimal places. - Answer Correct answers:standard
deviation=0.02
To find the sample standard deviation of the land area for residential buildings, use
the following formula.
s=∑i(xi−x¯)2(n−1)−−−−−−−−−−−⎷
The variance, which is equal to the square of the standard deviation, is equal to the sum
of the squares of the deviations divided by one less then the sample size.
s2ss=∑(x−x¯)2n−1=0.00147854−−−−−−−−−√=0.0192
Therefore, after rounding to two decimal places, we find that the sample
standard deviation is about 0.02.
The following data set provides information of Households by Total Money
Income, Race, and Hispanic Origin of Householder.
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