The ages of two groups exercise at a local fitness center are listed below.
Group A: 37,36,32,41,42,36,44,45
Group B: 26,40,38,36,42,40,40,36
which statement about the data is true.
a. the mean age is the same for both groups
b. the range of ages is greater in group A than group B
c. the mode of the ages for both groups is 36
d. the median age is the same for both groups
c. the mode of the ages for both groups is 36
are you sure
Yes, I'm sure. In Group A, 36 appears twice and in Group B, 36 appears three times which means it is the mode for both groups.
in group b 36 appears two time not three times
To determine which statement about the data is true, let's analyze the information provided:
Group A: 37, 36, 32, 41, 42, 36, 44, 45
Group B: 26, 40, 38, 36, 42, 40, 40, 36
a. The mean age: To find the mean, we add up all the ages and divide by the total number of ages in each group.
Mean age of Group A:
(37 + 36 + 32 + 41 + 42 + 36 + 44 + 45) / 8 = 36.25
Mean age of Group B:
(26 + 40 + 38 + 36 + 42 + 40 + 40 + 36) / 8 = 37
Therefore, option a is incorrect because the mean age is not the same for both groups.
b. The range of ages: The range is the difference between the highest and lowest values in a set.
Range of ages for Group A: 45 - 32 = 13
Range of ages for Group B: 42 - 26 = 16
Therefore, option b is incorrect because the range of ages is greater in Group B, not Group A.
c. The mode of ages: The mode is the value that appears most frequently in a set.
In both Group A and Group B, the number 36 appears twice, making it the mode for both groups.
Therefore, option c is correct. The mode of the ages for both groups is 36.
d. The median age: The median is the middle value in a set of numbers when arranged in ascending order.
For Group A: 32, 36, 36, 37, 41, 42, 44, 45
The middle two values are 37 and 41, so the median is (37 + 41) / 2 = 39
For Group B: 26, 36, 36, 38, 40, 40, 40, 42
The middle two values are 38 and 40, so the median is (38 + 40) / 2 = 39
Therefore, option d is correct. The median age is the same for both groups.
To determine which statement is true, let's analyze the data for each statement:
a. To find the mean age for each group, we add up all the ages and divide by the number of ages.
Group A: (37 + 36 + 32 + 41 + 42 + 36 + 44 + 45) / 8 = 349 / 8 = 43.625
Group B: (26 + 40 + 38 + 36 + 42 + 40 + 40 + 36) / 8 = 298 / 8 = 37.25
Since the mean age of Group A (43.625) is not the same as the mean age of Group B (37.25), statement a is false.
b. To find the range of ages, we subtract the lowest age from the highest age.
Group A: Highest Age - Lowest Age = 45 - 32 = 13
Group B: Highest Age - Lowest Age = 42 - 26 = 16
The range of ages for Group B (16) is greater than the range for Group A (13), so statement b is true.
c. The mode represents the most frequently occurring age in a dataset.
Group A: 36 occurs twice, while no other age is repeated.
Group B: 40 occurs three times, while no other age is repeated.
The mode for both groups is not 36 but rather 40, so statement c is false.
d. The median represents the middle value in a sorted dataset.
Group A: Sorting the ages in ascending order: 32, 36, 36, 37, 41, 42, 44, 45. The median is 37.
Group B: Sorting the ages in ascending order: 26, 36, 36, 38, 40, 40, 40, 42. The median is 38.
Since the medians for both groups (37 and 38) are not the same, statement d is false.
In summary, the only true statement is b. The range of ages is greater in Group B than Group A.