Here is our sample data, x = [2, 6, 8, 1, 56, 13, 8, -5, 4, 6, 23].\ Length, n = 11.
Average of the data. Add all items, divide by length to calculate mean. For x, mean = 11 (rounded)
Most common item. For x, mode = 6.
The median is the middle number in a data set. Steps to find the median-
Here, since n is 11, 6th item is the median = 6.
Quartiles are values that divide the data in 4 regions. The regions are known as the lowest 25% of numbers, next lowest 25% of numbers(up to median), second highest 25% of numbers (above median), the highest 25% of numbers. So to have 4 region, we need 3 points called as Q1,Q2,Q3. In layman’s term, the Q1 is greater than or equal to the lowest 25% of the number and so on. To calculate quartiles, data have to be sorted.
For x, Q1 = 2
It’s the same as median which is 6.
For x, Q3 = 13
It explains how far the data is spread out from their mean. Calculated as the average of the squared difference from the mean. For x, do \((2-11)^{2}+ (6-11)^{2} + .... + (23-11)^{2}\) and finally divide the sum by 11. Result is, 247.90
This is simply the square root of variance. Explains if a number is normal or not, a number can be big or small compared to the other items of the dataset. SD tells us how tightly the data is clustered around the mean. A small SD indicates that the data is tightly clustered. A large SD tells that the data is more spread apart.
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