"Love Statistics" notes (ii) Understanding variability

Variability (also known as walking or dispersion) can be seen as a measure of the difference between different values.

It may be more accurate to think of variability as the degree to which each value differs from a particular value. So which "value" do you think might be used as that particular value? Typically, this particular value is the mean value. As a result, variability becomes the number of differences between each value and the mean in the measurement data set.

The three quantities of variability are typically used to reflect the variability, dispersion, or dispersion of a set of data. These three quantities are the extreme difference, the standard deviation, and the variance.

Our initial normal idea might be to calculate the mean value of the data set, and then subtract each value with the mean. The average of these distances is then calculated. But it doesn't really work, for instance.

Array: 5,8,5,4,6,7,8,8,3,6

The mean value of this array is 6, then the mean minus each value ( -1+2-1-2+0+1+2+2-3+0) result is 0 according to our idea

In fact, most of the results of this method are zero, so we need to find a way to eliminate the minus sign, so that the result is not zero.

Calculate the extreme difference:

The extreme difference is the most general measure of variability. The extreme difference allows you to understand how the values differ from each other. The extreme difference is calculated by subtracting the minimum value from the maximum value in the data distribution.

In general, the very poor formula is as follows: R = H-l

where r is the extreme difference, H is the maximum value in the dataset, and L is the minimum value in the data set.

Calculate standard deviation:

The most commonly used variability amount is the standard deviation.

The standard deviation (abbreviated to S or SD) represents the average number of variability in a data set. The actual meaning is the average distance from the mean.

The larger the standard deviation, the greater the average distance between each data point and the mean of the data distribution.

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which

S is the standard deviation

∑ is Sigma, which means that all subsequent values are summed

X is the specific value

X on a horizontal line is the mean value of all data

n is the sample size

1) List each value. How values are sorted doesn't matter

2) Calculate the mean value of the data set

3) minus the mean value for each value

4) calculates the square of each difference.

5) calculates the sum of squares of deviations of all and mean values.

6) squared divided by n-1

7) Calculate square root

• As a measure of variability, the standard deviation can tell us the average deviation of each value of the data set from the mean.

• The standard deviation is calculated as the average distance from the mean value of the deviation. Therefore, you first need to calculate the mean value as the amount of the concentration trend. Therefore, it is not necessary to waste time on the median and the majority when calculating the standard deviation.

• The larger the standard deviation, the wider the numerical distribution, the greater the difference between the values

• As with the mean, standard deviation is sensitive to extreme values. When you calculate the standard deviation of a sample, if there is an extremum in the data, you need to report it in the data.

• If the s=0, there is absolutely no variability in the data set, and the value is exactly the same, this situation rarely occurs.

Variance:

Variance is the square of the standard deviation.

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"Love Statistics" notes (ii) Understanding variability