The range is the simplest measure of dispersion to calculate

Range =

The range, like the mean, has the disadvantage of being sensitive to outliers.

Another disadvantage of using the range is that its calculation is based on ......... values only

Thus, the range is a very satisfactory measure of dispersion

the most common measures of variability describe the extent to which the sample observations deviate from the sample mean 𝑥᪄.

A particular deviation is .......... if the corresponding 𝑥 value is greater than 𝑥شرطه and ............. if the 𝑥 value is less than 𝑥شرطه᪄.

The greater the amount of variability in the sample, the larger themagnitudes (ignoring the signs) of the deviations

The standard deviation is the most-used measure of dispersion

The value of the standard deviation tells how closely the values of a data set are clustered around the median.

The standard deviation is obtained by taking the negative square root of the variance

The variance calculated for population data is denoted by 𝝈^2and the variance calculated for sample data is denoted by 𝑠^2

𝝈^𝟐 = 𝛴(𝑥 − 𝜇)^2 / 𝑁

The values of the variance and the standard deviation are never negative

Calculating Mean for Grouped Data
Mean for population data: 𝜇 =Σ𝑚f / N

mean =

VARIANCE AND STANDARD DEVIATION FOR GROUPED DATA
𝝈^𝟐 =𝜮𝒇(𝒎−𝝁)^𝟐 /𝑵

Chebyshev's theorem : gives a ......... bound for the area under a curve between ........ points that are on opposite sides of the mean and at the same distance from the mean.

Chebyshev'sTheorem : For any number 𝑘 Smaller than 1

Chebyshev'sTheorem = (1 − 1/𝑘^2)