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=
try this data set:
9,9,9,9,9,9, -9,-9,-9,-9,-9,-9
mean: zero
median: zero
standard deviation: ;you figure it.
Ok, I know your thinking: But it says 5 data points.
9,9,0,-9,-9
do the statistics.
What you are missing is an understanding of numbers. Numbers are symbols, they do not indicate value or meaning. Any statistician can shift the numbers (mean, median, and standard deviation) by changing the scale, or sample range.
Do the same math in these numbers:
29,29, 20, 11,11
same data, shifted. Interesting, isn't it.
To create a dataset with the desired criteria, we need to carefully select the five values. Let's assume the values {1, 2, 3, 7, 10}.
Mean:
The mean is calculated by summing up all the values in the dataset and then dividing by the total number of values.
Mean = (1 + 2 + 3 + 7 + 10) / 5 = 23 / 5 = 4.6
Median:
The median is the middle value in a dataset when the values are sorted in ascending order.
The values are already sorted, and in this case, the middle value is 3.
Median = 3
Standard Deviation:
The standard deviation is a measure of the dispersion or spread of the dataset. To calculate it, we will first find the deviation of each value from the mean, square the deviations, find the sum of the squared deviations, divide it by the total number of values, and finally take the square root of the result.
Deviation for each value: (-3.6, -2.6, -1.6, 2.4, 5.4)
Squared deviations for each value: (12.96, 6.76, 2.56, 5.76, 29.16)
Sum of squared deviations: 57.20
Standard Deviation = sqrt(57.20 / 5) = sqrt(11.44) ≈ 3.38
Therefore, the dataset and its statistics are as follows:
Values: {1, 2, 3, 7, 10}
Mean: 4.6
Median: 3
Standard Deviation: 3.38