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)

empirical rule applies only to a specific type of distribution called a bell - shaped distribution

The 𝒛 score corresponding to a particular value is

measure of position determines the position of a multi value in relation to other values in a sample or a population data set.

Quartiles are the summary measures that divide a ranked data set into four equal parts.