ECON 214: Measures of Variability

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Questions and Answers

Which measure of dispersion is particularly suitable for skewed data?

Coefficient of variation

Range

Standard deviation

Semi-interquartile range (correct)

If two datasets have the same range, what can we conclude about their spread?

They have the same standard deviation.

They have the same distribution.

They have the same variance.

We cannot conclude anything definitive about their spread. (correct)

What is the primary reason the range is rarely used in scientific work?

It is only applicable to continuous data.

It is not a reliable measure of spread for large datasets.

It is difficult to calculate.

It is insensitive to outliers. (correct)

Which of the following statements about variance and standard deviation is TRUE?

Standard deviation is the square root of variance. Signup and view all the answers

Why is the semi-interquartile range (SIR) a good measure of dispersion for skewed data?

It is less affected by extreme values. Signup and view all the answers

Which of these scenarios would be most appropriate to use the range as a measure of dispersion?

Presenting the variability in sales figures for a company to a non-statistical audience. Signup and view all the answers

What does the coefficient of variation tell us about a dataset?

The relative spread of the data compared to the mean. Signup and view all the answers

Which measure of dispersion is most sensitive to outliers?

Range Signup and view all the answers

What is the Semi-Interquartile Range (SIR) for the given data set: 2, 4, 6, 8, 10, 12, 14, 20, 30, 60?

10 Signup and view all the answers

What is the range of the given data set: 2, 4, 6, 8, 10, 12, 14, 20, 30, 60?

58 Signup and view all the answers

Which of the following statements about variance is TRUE?

All of the above. Signup and view all the answers

If the variance of a data set is 16, what is the standard deviation?

4 Signup and view all the answers

What is the key difference between variance and standard deviation?

Both a and c. Signup and view all the answers

Which of the following is NOT a measure of dispersion?

Mean Signup and view all the answers

Which of the following statements about measures of dispersion is TRUE?

Measures of dispersion describe the spread or variability of a data set. Signup and view all the answers

A larger variance indicates that the data is:

More spread out from the mean. Signup and view all the answers

Which of the following measures indicates the degree of dispersion in a data set?

Standard Deviation Signup and view all the answers

What does a higher variance in a data set signify?

There is greater diversity in scores. Signup and view all the answers

Which statement best describes the semi-interquartile range?

It is half the difference between the third and first quartiles. Signup and view all the answers

In which scenario would the range of a data set be the most informative measure of variability?

When the dataset consists of a few extreme outliers. Signup and view all the answers

What typically occurs to the standard deviation if data values in a dataset are decreased by a constant?

It remains unchanged. Signup and view all the answers

What characterizes a distribution with low dispersion compared to one with high dispersion?

Low dispersion has a smaller range of scores. Signup and view all the answers

Study Notes

Session Overview

Continuation of descriptive statistics focusing on measures of variability.
Explores measures such as Range, Standard Deviation, and Variance.
Introduces concepts of position in data like interquartile range and percentiles.

Concept of Dispersion

Dispersion refers to the variety or diversity in data scores.
Greater dispersion indicates larger differences among scores.
Lower dispersion suggests scores are more similar.
More spread out distributions yield a higher measure of dispersion.
Example: Accra exhibits more diversity compared to Koforidua.
Normal distribution: Taller curves indicate less dispersion than flatter curves.

Measures of Dispersion

Main measures of dispersion include:
- Range
- Semi-Interquartile Range (SIR)
- Variance/Standard Deviation
- Coefficient of Variation

The Range

Defined as the difference between the largest (XL) and smallest (XS) scores: XL - XS.
Example calculation from data set {4, 8, 1, 6, 6, 2, 9, 3, 6, 9} results in a range of 8 (9 - 1).
Preferred for ordinal data or non-statistical audiences.
Rarely used in scientific contexts due to its insensitivity.
Notable limitation: Identical ranges can arise from distinct data sets.

The Semi-Interquartile Range (SIR)

Defined as half the difference between the first quartile (Q1, 25th percentile) and third quartile (Q3, 75th percentile): SIR = (Q3 - Q1) / 2.
Effective for skewed data as it is less affected by extreme values.

Variance and Standard Deviation

Most utilized measures of dispersion for interval or ratio variables.
Variance measures the average of squared deviations from the mean.

Variance

Calculated using the formula: σ² = Σ(X − μ)² / N.
Each score is adjusted by subtracting the mean, yielding deviation scores.
Squared deviations ensure all values are non-negative.
Interpretation: Larger variance indicates greater average deviation from the mean; smaller variance indicates lesser deviation.

Standard Deviation

Represents the square root of the variance, providing dispersion in original units.
Provides insight into how scores are spread around the mean.

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Description

This session continues descriptive statistics, covering measures of variability such as range, standard deviation, and variance. It's part of ECON 214 course on elements of statistics for economists.