From the following list of number of discharges each day in September, compute the mean, median, mode, and range. Round the mean and median to one decimal point.
Day # of discharges
1 27
2 22
3 35
4 63
5 42
6 55
7 62
8 65
9 32
10 35
11 36
12 75
13 65
14 84
15 37
16 38
17 62
18 65
19 48
20 55
21 53
22 59
23 54
24 52
25 32
26 64
27 67
28 69
29 58
30 55
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To compute the mean, median, mode, and range from the given list of the number of discharges each day in September, follow these steps:
1. Mean:
Add up all the numbers in the list.
27 + 22 + 35 + 63 + 42 + 55 + 62 + 65 + 32 + 35 + 36 + 75 + 65 + 84 + 37 + 38 + 62 + 65 + 48 + 55 + 53 + 59 + 54 + 52 + 32 + 64 + 67 + 69 + 58 + 55 = 1,647
Divide the sum by the total number of days (30).
1,647 / 30 = 54.9 (rounded to one decimal point)
The mean of the number of discharges each day in September is 54.9.
2. Median:
Arrange the numbers in ascending order.
22, 27, 32, 32, 35, 35, 36, 37, 38, 42, 48, 52, 53, 54, 55, 55, 55, 58, 59, 62, 62, 63, 64, 65, 65, 67, 69, 75, 84
Since the total number of days is even (30), there are two middle numbers.
They are the 15th and 16th number, which are both 55.
The median of the number of discharges each day in September is 55.
3. Mode:
Identify the number(s) that appear most frequently in the list.
The number 65 appears most frequently (3 times) in the list.
The mode of the number of discharges each day in September is 65.
4. Range:
Subtract the smallest number from the largest number in the list.
84 - 22 = 62.
The range of the number of discharges each day in September is 62.
Therefore, the mean is 54.9, the median is 55, the mode is 65, and the range is 62.
To compute the mean, median, mode, and range from the given list of number of discharges each day in September, follow these steps:
Mean:
1. Sum up all the numbers: 27 + 22 + 35 + 63 + ... + 55.
2. Divide the sum by the total number of values, which in this case is 30 (since there are 30 days in September).
3. Round the result to one decimal point.
Median:
1. Arrange the numbers in ascending order: 22, 27, 32, 32, 35, 35, 36, ... , 84.
2. Find the middle value. In this case, since there are 30 values, the median will be the average of the 15th and 16th values when arranged in ascending order.
3. Round the result to one decimal point.
Mode:
1. Identify the value(s) that appear most frequently in the given list.
2. If there is more than one mode (multiple values with the highest frequency), the data is multimodal. If no value repeats or all values appear equally, there is no mode.
Range:
1. Find the difference between the highest and lowest values in the list.
2. The highest value is 84, and the lowest value is 22.
3. Subtract the lowest value from the highest value to find the range.
Now let's compute the mean, median, mode, and range for the given list of number of discharges each day in September:
Mean:
(27 + 22 + 35 + 63 + ... + 55) / 30 = sum / 30 = mean
Sum of the values = 1476
Mean = 1476 / 30 = 49.2 (rounded to one decimal point)
Median:
Arranging the values in ascending order gives us: 22, 27, 32, 32, 35, 35, 36, ... , 84.
The middle two values are 55 and 57
Median = (55 + 57) / 2 = 56.0 (rounded to one decimal point)
Mode:
In this case, there is no mode since no value appears more than any other value.
Range:
Highest value: 84
Lowest value: 22
Range = Highest value - Lowest value = 84 - 22 = 62
Therefore, the mean is 49.2, the median is 56.0, there is no mode, and the range is 62.