Let's calculate the mean, median, mode, and range for each set of numbers.
1) The first set of numbers: 24, 31, 12, 38, 12, 15
Mean:
To find the mean, we add all numbers in the set and then divide by the count of the numbers.
Mean = (24 + 31 + 12 + 38 + 12 + 15) / 6
Mean = (132) / 6
Mean = 22
Median:
To find the median, we need to arrange the numbers in ascending order and then find the middle number. If there's an even number of observations, we find the average of the two middle numbers.
Ordered set: 12, 12, 15, 24, 31, 38
There's an even number of numbers (6), so the median is the average of the third and fourth numbers.
Median = (15 + 24) / 2
Median = 39 / 2
Median = 19.5
Mode:
The mode is the number that appears most frequently in the set.
In this set, 12 appears twice while all other numbers appear only once, so 12 is the mode.
Mode = 12
Range:
The range is the difference between the largest and the smallest numbers in the set.
Range = 38 (largest) - 12 (smallest)
Range = 26
2) The second set of numbers: 5, 28, 16, 32, 5, 16, 48, 29, 5, 35
Mean:
To find the mean, we add all numbers in the set and then divide by the count of the numbers.
Mean = (5 + 28 + 16 + 32 + 5 + 16 + 48 + 29 + 5 + 35) / 10
Mean = (219) / 10
Mean = 21.9
Median:
To find the median, we arrange the numbers in ascending order and then find the middle number. If there's an even number of observations, we find the average of the two middle numbers.
Ordered set: 5, 5, 5, 16, 16, 28, 29, 32, 35, 48
Again, there's an even number (10), so the median is the average of the fifth and sixth numbers.
Median = (16 + 28) / 2
Median = 44 / 2
Median = 22
Mode:
The mode is the number that appears most frequently in the set.
In this set, 5 appears three times, which is more frequent than any other number, making it the mode.
Mode = 5
Range:
The range is the difference between the largest and the smallest numbers in the set.
Range = 48 (largest) - 5 (smallest)
Range = 43
In summary:
For the first set (24, 31, 12, 38, 12, 15):
Mean: 22
Median: 19.5
Mode: 12
Range: 26
For the second set (5, 28, 16, 32, 5, 16, 48, 29, 5, 35):
Mean: 21.9
Median: 22
Mode: 5
Range: 43
