Chapter 3: Section 3.3 - Measures of Variation: Understanding Standard Deviation

What is the formula for the Maximum "Usual" Value of the Range Rule of Thumb?

(Mean) + 2 x (Standard Deviation)

What is the formula for the Minimum "Usual" Value of the Range Rule of Thumb?

(Mean) - 2 x (Standard Deviation)

List the properties of the Empirical Rule: 1) Approximately ____% of ________ (most or all) data values lie within ____ (#?) standard deviation of the __________ (Mean or Mode) 2) " 3) "

1) Approximately 68% of all data values lie within 1 standard deviation of the mean 2) Approximately 95% of all data values lie within 2 standard deviation of the mean 3) Approximately 99.7% of all data values lie within 3 standard deviations of the mean

Coefficient of Variation (CV)

A set of non-negative sample or population data describes the standard deviation relative to the Mean

According to the ________ ________ ____ ________, a data value is called ________ (usual or unusual) if it is within ____ (two or three) standard deviations of the ________ (Mean or Mode). Otherwise, the data value is called ________ (usual or unusual).

According to the Range Rule of Thumb, a data value is called Usual if it is within two standard deviations of the Mean. Otherwise, the data value is called Unusual.

Describe how the Harmonic Mean is found (Write out the formula).

By dividing the number of data values 'n' by the sum of the reciprocals of all data values

T or F: Values of 's' tend to underestimate the population Variance.

False - Values of 's' tend to underestimate the population Standard Deviation.

Range Rule of Thumb

For many data sets, the vast majority of data values lie within two standard deviations of the mean

List the Properties of Variance: 1) The value of the ________ (standard deviation or variance) is ________ (lower or greater) than or equal to ________ (#?). 2) The variance is equal to ________ (#?) if and only if ________ (most or all) data values are ________ (the same or different). 3) The units of the ________ (standard deviation or variance) are the square of the units of the original data values.

List the Properties of Variance: 1) The value of the variance is greater than or equal to zero. 2) The variance is equal to zero if and only if all data values are the same. 3) The units of the variance are the square of the units of the original data values.

Harmonic Mean

Often used as a measure of center for data sets consisting of rates of change, such as speeds

How do you compare Standard Deviations of two data sets when comparing Variation in Different Data sets?

One only compares standard deviations of two data sets if the data sets use the same scale and units and have roughly the same mean. Otherwise, use the coefficient of variation for comparison.

What is the Rounding Rule for the Coefficient of Variation?

Round the Coefficient of Variation to one decimal place

The ________ ____ ________ ( ___ ) for a set of non-negative sample or population data describes the standard deviation relative to the mean.

The Coefficient of Variation for a set of non-negative sample or population data describes the standard deviation relative to the Mean.

The ________ ________ is where the data sets having a distribution that is approximately bell-shaped tend to have some properties (listed on another set of cards).

The Empirical Rule is where the data sets having a distribution that is approximately bell-shaped tend to have some properties (listed on another set of cards).

The ________ ________ is often used as a measure of center for data sets consisting of rates of change, such as speeds.

The Harmonic Mean is often used as a measure of center for data sets consisting of rates of change, such as speeds.

The ________ ________ ____ ________ is for many data sets, the vast majority of data values lie within two standard deviations of the mean.

The Range Rule of Thumb is for many data sets, the vast majority of data values lie within two standard deviations of the mean.

The ________ ________ of a population is computed as follows: (formula on the opposite side of the flash card)

The Standard Deviation of a population is computed as follows:

The ________ of a data set is the square of the standard deviation: (formula on the opposite side of the flash card)

The Variance of a data set is the square of the standard deviation:

Empirical Rule

The data sets having a distribution that is approximately bell-shaped tend to have some properties (listed on another set of cards)

The sample standard deviation is a(n) ________ (Biased or Unbiased) Estimator of the population ________ (Standard Deviation or Variance).

The sample standard deviation is a Biased Estimator of the population standard deviation.

Biased Estimator

The sample standard deviation is of the population standard deviation

The sample variance is a(n) ________ (Biased or Unbiased) Estimator of the population ________ (Standard Deviation or Variance).

The sample variance is an Unbiased Estimator of the population Variance.

What are the Rounding Rules for the Range, Standard Deviation, and/or Variance?

When Rounding the value of the Range, Standard Deviation, or Variance, carry one more decimal place than is present in the original data set

What is the formula for the Consequence of the Range Rule of Thumb?

s ≈ (Range) / 4