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Questions and Answers
Questions and Answers
What is the formula for calculating the standard deviation (SD) of a sample?
What is the formula for calculating the standard deviation (SD) of a sample?
The formula for calculating the standard deviation (SD) of a sample is: $s = \sqrt{\frac{\sum(x_i - x)^2},{n}}$, where $s$ is the sample SD, $x$ is the sample mean, $x_i$ is the ith element from the sample, and $n$ is the number of elements in the sample.
Explain the concept of a negatively skewed distribution.
Explain the concept of a negatively skewed distribution.
In a negatively skewed distribution, the mass of the distribution is concentrated on the right, leading to a longer left tail. This means that there are more extreme values on the left side of the distribution, and the tail extends to the right.
What percentage of scores are typically within 1 standard deviation (SD) of the mean in a normal distribution curve?
What percentage of scores are typically within 1 standard deviation (SD) of the mean in a normal distribution curve?
In a normal distribution curve, about 68% of the scores are within 1 SD of the mean.
Describe the standard normal distribution curve.
Describe the standard normal distribution curve.
Explain the difference between descriptive and inferential statistics.
Explain the difference between descriptive and inferential statistics.
What is the formula for calculating the standard deviation (SD) of a sample?
What is the formula for calculating the standard deviation (SD) of a sample?
Describe the concept of a negatively skewed distribution.
Describe the concept of a negatively skewed distribution.
What percentage of scores are typically within 1 standard deviation (SD) of the mean in a normal distribution curve?
What percentage of scores are typically within 1 standard deviation (SD) of the mean in a normal distribution curve?
Explain the standard normal distribution curve.
Explain the standard normal distribution curve.
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Study Notes
Study Notes
Standard Deviation of a Sample
- The formula for calculating the standard deviation of a sample is:
- √(Σ(x - x̄)² / (n-1))
- where:
- x = individual data point
- x̄ = sample mean
- n = sample size
Negatively Skewed Distribution
- A negatively skewed distribution has a long tail on the left side of the mean.
- The mean is lower than the median and the mode.
- This indicates that there are more data points toward the higher end of the distribution, with a few outliers on the lower end.
Normal Distribution
- Approximately 68% of scores fall within 1 standard deviation of the mean in a normal distribution.
Standard Normal Distribution Curve
- The standard normal distribution curve is a bell-shaped curve with specific properties.
- It has a mean of 0 and a standard deviation of 1.
- This special case of the normal distribution is used for various statistical calculations and comparisons.
Descriptive vs Inferential Statistics
- Descriptive statistics summarize and describe data, while inferential statistics use sample data to draw conclusions about a larger population.
- Descriptive statistics include measures such as mean, median, mode, and standard deviation.
- Inferential statistics utilize tests like t-tests and ANOVA to generalize findings from samples to populations.
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