Invent a dataset with five values, with a mean smaller than the median and both the mean and median smaller than the standard deviation. give the data values and the statistics.
Mean=
Median=
Standard Deviation=
To invent a dataset with the given conditions, we need five values such that the mean is smaller than the median, and both the mean and median are smaller than the standard deviation.
Here is an example dataset:
Data values: 1, 2, 3, 9, 10
To find the statistics, let's calculate:
Mean:
The mean is calculated by adding up all the values and dividing by the total count.
Mean = (1 + 2 + 3 + 9 + 10) / 5 = 25 / 5 = 5
Median:
The median is the middle value of a sorted dataset. In this case, the numbers are already sorted.
Median = 3
Standard Deviation:
The standard deviation measures the spread of data. To calculate it, we need to find the squared difference between each value and the mean, sum them up, divide by the count (minus 1), and take the square root.
Step 1: Find the squared difference between each value and the mean:
(1 - 5)^2 = 16
(2 - 5)^2 = 9
(3 - 5)^2 = 4
(9 - 5)^2 = 16
(10 - 5)^2 = 25
Step 2: Sum up the squared differences:
16 + 9 + 4 + 16 + 25 = 70
Step 3: Divide by (count - 1):
70 / (5 - 1) = 70 / 4 = 17.5
Step 4: Take the square root:
Standard Deviation = √17.5 ≈ 4.18
Summary:
Mean = 5
Median = 3
Standard Deviation ≈ 4.18
Thus, this dataset satisfies the given conditions.