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Questions and Answers
A positive skew indicates that most students are taller with very few being short.
A positive skew indicates that most students are taller with very few being short.
False (B)
What shape does a normal distribution typically take when plotted?
What shape does a normal distribution typically take when plotted?
- Line
- Bell curve (correct)
- Triangle
- Square
What statistical tests can be used to check if data is normally distributed?
What statistical tests can be used to check if data is normally distributed?
Kolmogorov-Smirnov and Shapiro-Wilk
A ____ kurtosis indicates that the data is very peaked.
A ____ kurtosis indicates that the data is very peaked.
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Match the following terms with their definitions:
Match the following terms with their definitions:
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Why is normal distribution important in statistics?
Why is normal distribution important in statistics?
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Study Notes
Normal Distribution
- Most students' heights cluster around the average, creating a bell-shaped curve when graphed.
- This bell curve is an indicator of a normal distribution.
Skewed Data
- Positive skew occurs when most students are shorter, with a few very tall students inflating the average.
- Negative skew arises when most students are taller, with a few very short students lowering the average.
Kurtosis
- Kurtosis gauges the "peakedness" of a data distribution.
- High kurtosis indicates a sharper peak, suggesting more data points are close to the mean.
- Low kurtosis implies a flatter distribution, with data points more spread out.
Importance of Normal Distribution
- Many statistical tests rely on the assumption that data follows a normal distribution.
- Non-normal data can lead to inaccurate results in statistical analyses.
Checking for Normal Distribution
- A histogram can visually determine if data approximates a bell curve.
- Statistical tests like Kolmogorov-Smirnov and Shapiro-Wilk can quantitatively assess normality.
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