Range & interquartile range
Range The range is found by subtracting the smallest value from the largest value.
Interquartile range The interquartile range is found by subtracting the lower quartile from the upper quartile, so I. Q. R. = Q3 – Q1
Variance and standard deviation
Variance is the square of the standard deviation .
σ^{2 }= \(\frac{1}{n}\) \(\sum_{i = 1}^n\)(x_{i} – x)^{2}f_{i}
σ^{2 }= \(\frac{1}{n}\) \(\sum_{i = 1}^n\)x_{i} ^{2}f_{i}– x^{2}
Variance and standard deviation measure the spread of the distribution.
Rough checks ,x ̅± 1σ, x ̅±2σ ,
When calculating a standard deviation, you should check that there is approximately 65 − 70% of the population within 1 s.d. of the mean and
approximately 95% within 2 s.d. of the mean.
These approximations are best for a fairly symmetrical distribution.
Coding and variance
Using the coding t_{1} , \(\frac{x_i - k}{a}\)we see that
x_{1 } = at_{1} + k
And σ_{x}^{2} = a^{2} σ_{t}^{2}
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