Statistics Unit Test
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Question
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, 2, and 3
statements 1, 2, and 3
statements 2 and 3
statements 2 and 3
statements 1 and 2
statements 1 and 2
statements 1 and 3
statements 1 and 3
choose an answer.
The answer is: statements 1 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)
Population: all players in the softball league
Sample: the 45 players Maritza asked about basketball
Size of population: 225 players
Size of sample: 45 players
show your work
Population size: Given in the problem, the population size is 225 players.
Sample size: Maritza chooses 45 players from the softball league to ask about basketball, making the sample size 45 players.
To determine which statement is true, let's calculate the mean, median, and range for both Company A and Company B.
Company A: 34, 28, 36, 27, 45, 44, 30, 42, 41, 40, 50, 48, 52, 45, 39, 38
Finding the mean:
Mean = (Sum of all ages) / (Number of ages)
Mean of Company A = (34 + 28 + 36 + 27 + 45 + 44 + 30 + 42 + 41 + 40 + 50 + 48 + 52 + 45 + 39 + 38) / 16
Mean of Company A = 640 / 16
Mean of Company A = 40
Finding the median:
Median is the middle value when the ages are arranged in ascending order.
Arranging the ages of Company A in ascending order: 27, 28, 30, 34, 36, 38, 39, 40, 41, 42, 44, 45, 45, 48, 50, 52
Median of Company A = (40th age + 41st age) / 2
Median of Company A = (40 + 41) / 2
Median of Company A = 81 / 2
Median of Company A = 40.5
Finding the range:
Range = Maximum age - Minimum age
Range of Company A = 52 - 27
Range of Company A = 25
Now let's do the same calculations for Company B:
Company B: 29, 32, 48, 51, 49, 37, 33, 35, 36, 40, 45, 48, 43, 43, 44, 48
Mean of Company B ≈ 40.25
Median of Company B ≈ 41
Range of Company B ≈ 22
Comparing the results:
Statement 1: The mean age of employees from Company A is higher than the mean age of employees from Company B.
This statement is false since the mean of Company A (40) is lower than the mean of Company B (40.25).
Statement 2: The median age of employees from Company A is lower than the median age of employees from Company B.
This statement is false since the median of Company A (40.5) is higher than the median of Company B (41).
Statement 3: The range of ages of employees from Company A is higher than the range of ages of employees from Company B.
This statement is true since the range of Company A (25) is higher than the range of Company B (22).
Therefore, the correct answer is:
statements 1 and 3
To determine which statement is true, we need to calculate the mean, median, and range of ages for employees from both Company A and Company B.
To find the mean, sum up all the ages and divide by the total number of employees. For Company A, the sum of ages is 34 + 28 + 36 + 27 + 45 + 44 + 30 + 42 + 41 + 40 + 50 + 48 + 52 + 45 + 39 + 38 = 637. Since there are 16 employees in Company A, the mean age is 637 / 16 = 39.81 (rounded to two decimal places). For Company B, the sum of ages is 29 + 32 + 48 + 51 + 49 + 37 + 33 + 35 + 36 + 40 + 45 + 48 + 43 + 43 + 44 + 48 = 625. Since there are 16 employees in Company B, the mean age is 625 / 16 = 39.06 (rounded to two decimal places).
To find the median, we need to arrange the ages in ascending order and find the middle value. For Company A, the ages in ascending order are 27, 28, 30, 34, 36, 38, 39, 40, 41, 42, 44, 45, 45, 48, 50, 52. The middle value is 42. For Company B, the ages in ascending order are 29, 32, 33, 35, 36, 37, 40, 43, 43, 44, 45, 48, 48, 49, 51, 52. The middle value is also 42.
To find the range, subtract the minimum age from the maximum age. For Company A, the minimum age is 27 and the maximum age is 52, so the range is 52 - 27 = 25. For Company B, the minimum age is 29 and the maximum age is 52, so the range is 52 - 29 = 23.
Based on the calculations:
- The mean age of employees from Company A is 39.81 and from Company B is 39.06. So, statement 1 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 42 and from Company B is 42. So, statement 2 is false, the median age of employees from Company A is not lower than the median age of employees from Company B.
- The range of ages of employees from Company A is 25 and from Company B is 23. So, statement 3 is false, the range of ages of employees from Company A is not higher than the range of ages of employees from Company B.
Therefore, the correct answer is "statements 1 and 2."