Question

bill os examining the variability in ethnoracial diversity by state. which measure of variability would bill ise amd why

Answer 1

Variability :

Variability is used to observe the spread of the data set and variability shows how much the data varying from the central value. Variability is also referred to as dispersion. Variability is used to compare the data set with other data sets.

Measures of variability:

The measures of variability are given below:

• Range

• Inter-quartile range

• Standard deviation

• Variance

Range:

The range is obtained by subtracting the lowest value from the highest value in the set of data.

Formula for range:

Range = L – S. Here, L is largest value and S is the smallest value in the data set.

Example:

Find the range for following values:

Data values: 10, 9, 25, 59, 1, 36, 62, 49, 71 and 38.

Here, the largest value is 71 and the smallest value is 1.

Hence, the range is,

Thus, the range for the given values is 70.

Inter-quartile range:

Inter-quartile range is obtained by subtracting the first quartile from the third quartile.

Formula for inter-quartile range is .

Here, Q3 represents the third quartile and Q1represents the first quartile.

Quartiles:

Values which divide the data into four parts are called as quartiles. These quartiles include a lower quartile (Q1), a median (Q2) and an upper quartile (Q3).

Standard deviation and Variance:

Both the standard deviation and the variance are based on how much each observation deviates from a central point (mean). In general, the greater the distances between the individual observations and the mean, the greater the variability of the data set. Standard deviation is called as root mean square deviation. It is denoted by σ. Moreover, the variance is obtained by squaring the standard deviation. Usually the variance denoted by σ2.

Formula for standard deviation is, .

Formula for variance is,

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