These are the scores for two randomly selected lacrosse teams. Find the range of the number of goals scored by each team. Based on the range, which team has a more consistent number of goals scored?
This table shows the scores of two lacrosse teams across six games.
Lacrosse Team 1: 6 0 4 17 3 12
Lacrosse Team 2: 23 14 22 14 17 22
(2 points)
The range of the number of goals scored by Lacrosse Team 1 is
. The range of the number of goals scored by Lacrosse Team 2 is
. Based on the range, Lacrosse Team
has a more consistent number of goals scored.
Use the image to answer the question.
An illustration shows two sets of dot plots. One is titled Gas Mileage in miles per gallon, Cars and the other is Gas Mileage in miles per gallon, S U Vs. The plots are shown as dots in a vertical row over each number on a number line. For Cars, a number line with arrows on both ends ranges from 18 to 22 in increments of 1. There is 1 dot above 18, 2 dots above 19, 3 dots above 20, 2 dots above 21, and 1 dot above 22. For S U Vs, a number line with arrows on both ends ranges from 21 to 25 in increments of 1. There is 1 dot above 21, 1 dot above 22, 2 dots above 23, 2 dots above 24, and 3 dots above 25.
The dot plots show the gas mileage for randomly selected cars and SUVs. Which data values do both distributions have in common?
(1 point)
The data value in common for both distributions with the lowest number is
.
The data value in common for both distributions for the highest number is.
Fifteen students are randomly selected from two different classes. They were asked how many books they read during the summer. Their responses are as follows. Find the median number of books read by each class. Which class has a higher median number of books read?
Class 1: 0, 5, 3, 6, 7, 8, 10, 1, 1, 4, 5, 6, 4, 5, 6
Class 2: 2, 2, 4, 3, 0, 0, 6, 7, 10, 9, 6, 5, 3, 1, 2
(2 points)
The median number of books read during the summer by Class 1 is
.
The median number of books read during the summer by Class 2 is
.
Class
has a higher median number of books read during the summer.
The ages of randomly selected employees at two companies are recorded. Their ages are as follows.
Company A: 34, 28, 36, 27, 45, 44, 30, 42, 41, 40, 50, 48, 52, 45, 39, 38
Company B: 29, 32, 48, 51, 49, 37, 33, 35, 36, 40, 45, 48, 43, 43, 44, 48
Which of the following statements is true?
The mean age of employees from Company A is higher than the mean age of employees from Company B.
The median age of employees from Company A is lower than the median age of employees from Company B.
The range of ages of employees from Company A is higher than the range of ages of employees from Company B.
(1 point)
Responses
statements 1 and 2
statements 1 and 2
statements 1, 2, and 3
statements 1, 2, and 3
statements 1 and 3
statements 1 and 3
statements 2 and 3
Maritza plays in a softball league. She wants to know about how many players in the league also play basketball. Because there are 225 players in the league, she chooses the names of 45 of the players and asks them whether they also play basketball. Describe the population and the sample. What is the size of the population, and what is the size of the sample? Show your work.(2 points)
1 answer
Problem 1: Lacrosse Teams
Scores:
- Lacrosse Team 1: 6, 0, 4, 17, 3, 12
- Lacrosse Team 2: 23, 14, 22, 14, 17, 22
Calculating Range:
- The range is calculated by subtracting the minimum score from the maximum score.
-
Lacrosse Team 1:
- Minimum = 0
- Maximum = 17
- Range = 17 - 0 = 17
-
Lacrosse Team 2:
- Minimum = 14
- Maximum = 23
- Range = 23 - 14 = 9
Conclusion:
Based on the ranges:
- Lacrosse Team 1: Range = 17
- Lacrosse Team 2: Range = 9
Lacrosse Team 2 has a more consistent number of goals scored, as it has a smaller range.
Problem 2: Gas Mileage
Dot Plots:
- Cars: 18 (1), 19 (2), 20 (3), 21 (2), 22 (1)
- SUVs: 21 (1), 22 (1), 23 (2), 24 (2), 25 (3)
Common Values:
- Both distributions share the numbers 21 and 22.
Conclusion:
The data value in common for both distributions with the lowest number is 21. The data value in common for both distributions for the highest number is 22.
Problem 3: Median Number of Books
Responses:
- Class 1: 0, 5, 3, 6, 7, 8, 10, 1, 1, 4, 5, 6, 4, 5, 6 (sorted: 0, 1, 1, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 8, 10)
- Class 2: 2, 2, 4, 3, 0, 0, 6, 7, 10, 9, 6, 5, 3, 1, 2 (sorted: 0, 0, 0, 1, 2, 2, 2, 3, 4, 5, 6, 6, 7, 9, 10)
Finding the Median:
-
Class 1:
- Total numbers = 15 (odd)
- Median = 5 (the 8th number in sorted order)
-
Class 2:
- Total numbers = 15 (odd)
- Median = 3 (the 8th number in sorted order)
Conclusion:
The median number of books read during the summer by Class 1 is 5. The median number of books read during the summer by Class 2 is 3. Class 1 has a higher median number of books read.
Problem 4: Employee Ages
Ages:
- Company A: 34, 28, 36, 27, 45, 44, 30, 42, 41, 40, 50, 48, 52, 45, 39, 38 (sorted: 27, 28, 30, 34, 36, 38, 39, 40, 41, 44, 45, 45, 48, 50, 52)
- Company B: 29, 32, 48, 51, 49, 37, 33, 35, 36, 40, 45, 48, 43, 43, 44, 48 (sorted: 29, 32, 33, 35, 36, 37, 40, 43, 43, 44, 45, 48, 48, 49, 51)
Mean and Median Calculation:
-
Mean Age:
- Company A Total: (sum = 669) / 16 = 41.8125
- Company B Total: (sum = 699) / 16 = 43.6875
-
Median Age:
- Company A Median (8th and 9th numbers): (40 + 41) / 2 = 40.5
- Company B Median (8th and 9th numbers): (43 + 44) / 2 = 43.5
Conclusion:
- The mean age of employees from Company A is lower than the mean age of employees from Company B.
- The median age of employees from Company A is lower than the median age of employees from Company B.
- The range for Company A: 52 - 27 = 25; for Company B: 51 - 29 = 22.
Thus, the true statement from the options provided is statements 2 and 3.
Problem 5: Population and Sample
Describing Population and Sample:
- Population: All 225 players in the league.
- Sample: The 45 players selected by Maritza to survey.
Sizes:
- Size of the population = 225
- Size of the sample = 45
Conclusion:
Population size is 225, and sample size is 45.
