1. When the measure of spread is compared between two data sets, data set A has an interquartile range of 12, and data set B has an interquartile range of 23. How do the values of data set A compare to data set B?
A. The values of data set A are more spread out compared to the values of data set B.
B. The values of data set A are less spread out compared to the values of data set B.
C. The values of data set A are about the same on average as the values of data set B.
D. The values of data set A are less on average compared to the values of data set B.
2. A manager of a gift shop examines the number of sales that are made each day. She then compares the number of sales for each day in September and October by constructing the five-number summary for each month. The results are shown in the accompanying table.
September October
Minimum 112 131
First Quartile 154 149
Median 162 158
Third Quartile 171 167
Maximum 184 182
A. The number of sales made each day in September is slightly greater on average compared to the number of sales made each day in October. The spread of the data is similar between the two months using the interquartile range. However, there is an outlier for the month of September.
B. The number of sales made each day in October is slightly greater on average compared to the number of sales made each day in September. The spread of the data for September is greater than that for October based on the range.
C. The number of sales made each day in September is significantly greater on average compared to the number of sales made each day in October. The spread of the data is similar between the two months using the interquartile range. However, there is an outlier for the month of October.
D. The number of sales made each day in October is much greater on average compared to the number of sales made each day in September. The spread of the data for October is about twice of the spread for September based on the interquartile range.
3. Traffic engineers are measuring the number of vehicles per hour traveling on a road during peak times. A traffic counter is set up on the westbound lane and the eastbound lane. The results are shown in the accompanying box plots.
Which conclusion could be made about the number of vehicles traveling per hour for the westbound and eastbound lanes?
A. The number of vehicles traveling on the eastbound lane per hour during peak times is much greater compared to the westbound lane. The number of vehicles traveling on the westbound lane per hour during peak times has a significantly greater spread compared to the eastbound lanes. There are no outliers.
B. The number of vehicles traveling on the eastbound lane per hour during peak times is greater on average compared to the westbound lane. The number of vehicles traveling on the eastbound lane per hour during peak times has a slightly greater spread compared to the westbound lanes. The minimum for the eastbound data is an outlier.
C. The number of vehicles traveling on the westbound lane per hour during peak times is slightly greater on average compared to the eastbound lane. The number of vehicles traveling on the eastbound lane per hour during peak times has a greater spread compared to the westbound lanes. There are no outliers.
D. The number of vehicles traveling on the eastbound lane per hour during peak times is the same on average compared to the westbound lane. The number of vehicles traveling on the westbound lane per hour during peak times has a slightly greater spread compared to the eastbound lanes. The minimum for the westbound data is an outlier.
4. An administrator for the Department of Youth and Children is comparing the number of cases each case worker in the department has between 2019 and 2020. The results are provided in the accompanying table.
2019 14 15 14 15 13 14 19 17 13 16
2020 13 16 15 15 14 15 15 17 14 16
Interpret how the shape of the distribution for 2019 compares to the shape of the distribution for 2020.
A. The distribution for 2019 is skewed right, and the distribution for 2020 is skewed left. One case worker had an unusually high number of cases in 2019, while one case worker had an unusually low number of cases in 2020.
B. The distribution for 2019 is symmetric, and the distribution for 2020 is skewed right. One case worker had an unusually high number of cases in 2020.
C. Both distributions are skewed right. One case worker had an unusually high number of cases in 2019 and in 2020.
D. The distribution for 2019 is skewed right, and the distribution for 2020 is symmetric. One case worker had an unusually high number of cases in 2019.
5. Several pitchers in a certain professional baseball league claimed that the baseballs used during the 2019 season were "juiced." One pitcher compiled the number of home runs hit by each team in the league for the 2018 and 2019 seasons. The results are shown in the table below.
6. 2018 2019
176 175 167 220 249 256
172 210 235 227 224 279
128 218 170 146 250 242
186 157 162 215 163 219
133 205 191 167 210 231
How do the number of home runs hit by each team in 2018 compare to the number of home runs hit in 2019?
A. The number of home runs hit by each team in 2019 is about the same on average compared to the number of home runs hit by each team in 2018. The spread for the number of home runs hit by each team in 2019 is also about the same compared to 2018 when using the standard deviation.
B. The number of home runs hit by each team in 2019 is much greater on average compared to the number of home runs hit by each team in 2018. The spread for the number of home runs hit by each team in 2019 is also much greater compared to 2018 when using the standard deviation.
C. The number of home runs hit by each team in 2018 is slightly greater on average compared to the number of home runs hit by each team in 2019. The spread for the number of home runs hit by each team in 2018 is slightly greater compared to 2019 when using the interquartile range.
D. The number of home runs hit by each team in 2019 is slightly greater on average compared to the number of home runs hit by each team in 2018. However, the spread for the number of home runs hit by each team in 2019 is about the same compared to 2018 when using the standard deviation.
1. B. The values of data set A are less spread out compared to the values of data set B, since the interquartile range is smaller in data set A than in data set B.
2. A. The number of sales made each day in September is slightly greater on average compared to the number of sales made each day in October. The spread of the data is similar between the two months using the interquartile range. However, there is an outlier for the month of September, since the minimum value is quite a bit lower than the first quartile.
3. A. The number of vehicles traveling on the eastbound lane per hour during peak times is much greater compared to the westbound lane. The number of vehicles traveling on the westbound lane per hour during peak times has a significantly greater spread compared to the eastbound lane, since the interquartile range for the westbound lane is much larger than for the eastbound lane.
4. A. The distribution for 2019 is skewed right, and the distribution for 2020 is skewed left. One case worker had an unusually high number of cases in 2019, while one case worker had an unusually low number of cases in 2020.
5. D. The number of home runs hit by each team in 2019 is slightly greater on average compared to the number of home runs hit by each team in 2018. However, the spread for the number of home runs hit by each team in 2019 is about the same compared to 2018 when using the standard deviation.
How does the shape and size of rotors affect the efficiency of wind turbines?
The shape and size of wind turbine rotors can significantly impact their efficiency. Generally, larger rotors with a greater surface area are capable of capturing more wind energy and generating more electricity. However, larger rotors also require more structural support and can be more expensive and difficult to manufacture, install and maintain.
The shape of the rotor blades also plays a crucial role in the efficiency of wind turbines. A more curved blade allows for greater lift and therefore generates more energy, but it can also create more drag, which can reduce efficiency. A flatter blade may create less lift but could be more efficient in low wind speeds.
Overall, the shape and size of wind turbine rotors must be carefully designed and optimized to strike a balance between capturing the maximum amount of energy and maintaining efficiency and cost-effectiveness.