Chapter 6 Summary
Key Concepts Summary
- 6.1 Descriptive Statistics
- Differentiating Population and Sample
- Differentiating Quantitative and Continuous variables
- 6.2 Frequency Distribution and Histograms
- Creating and interpreting frequency tables
- Displaying, analyzing, and interpreting data in histograms
- 6.3 Descriptive Measures
- Calculating the Measures of Center and Measures of Dispersion for sets of data
- 6.4 Skewness
- Identifying the shape of a data set
- 6.5 Measures of Location
- Recognize, describe, calculate, and interpret the measures of location of data: quartiles and percentiles.
- 6.6 Graphical Representation
- Using graphs and charts to visualize data
Glossary of Terms
Central Limit Theorem. A theorem stating that as a sample size increases the sample mean will grow closer to normal.
Continuous Variable. A variable with an infinite number of possible values.
Frequency or relative frequency. (or percent frequency or probability).
Histogram. A visual display of a frequency chart.
Measures of Center. Measurements used to determine the center of data.
Measures of Dispersion. Measurements used to determine the spread of data.
Median. A number that measures the “center” of the data.
Normal Distribution. A “bell-shaped” symmetric distribution of data that can be used for estimating probabilities and proportions within a population.
Percentiles. Numbers that separate the (ordered) data into hundredths.
Population. A group to be studied.
Quantitative variable. A variable with a finite and countable number of possible values.
Quartiles. Numbers that separate the data into quarters.
Sample. A selection from the population.
Skew. A term to describe a curve that does not meet the criteria of a normal distribution.
Variable. The characteristics to be studied from the population and/or sample.
Formula & Symbol Hub
Symbols Used
- [latex]\mu[/latex] = Population Mean
- [latex]\bar{x}[/latex] = Sample Mean
- [latex]σ^2[/latex] = Population Variance
- [latex]s^2[/latex] = Sample Variance
- [latex]\sigma[/latex] = Population standard deviation
- [latex]s[/latex] = Sample standard deviation
- [latex]s_{\bar{x}}[/latex] = Standard error of the means
- [latex]z[/latex] = a Z-score
Formulas Used
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Formula 6.1 – Population Mean
[latex]\begin{align*}\mu&=\frac{\sum x_i}{N}\end{align*}[/latex]
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Formula 6.2 – Sample mean
[latex]\begin{align*}\bar{x}&=\frac{\sum x_i}{n}\end{align*}[/latex]
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Formula 6.3 – Population Variance
[latex]\begin{align*}\sigma^2=\frac{\sum\left(x_i-\mu\right)^2}{N}\end{align*}[/latex]
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Formula 6.4 – Sample Variance
[latex]\begin{align*}s^2=\frac{\sum\left(x_i-\bar{x}\right)^2}{n-1}=\frac{\Sigma x_i^2-\frac{\left(\sum x_i\right)^2}{n}}{n-1}\end{align*}[/latex]
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Formula 6.5 – Population Standard Deviation
[latex]\sigma=\sqrt{\sigma^2}[/latex]
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Formula 6.6 – Sample Standard Deviation
[latex]s=\sqrt{s^2}[/latex]
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Formula 6.7 – Standard Error of the Means
[latex]\begin{align*}s_{\bar{x}}=\sqrt{\frac{s^2}{n}}=\frac{s}{\sqrt{n}}\end{align*}[/latex]
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Formula 6.8 – Coefficient of Variation (Population)
[latex]\begin{align*}CV=\frac{\sigma}{\mu}\times 100\end{align*}[/latex]
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Formula 6.9 – Coefficient of Variation (Sample)
[latex]\begin{align*}CV=\frac{s}{\bar{x}}\times 100\end{align*}[/latex]
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Formula 6.10 – Interquartile Range
