Standard Deviation
Definition
The standard deviation measures the average amount of variation or dispersion in a set of data. It tells us how spread out the values are from the mean.
Analogy
Imagine you have two groups of friends, one group where everyone is roughly the same height and another group where people have very different heights. The standard deviation would be low for the first group because there is not much variation in height, while it would be high for the second group because there is a lot of variation in height.
Related terms
Variance: Variance is another measure of variability that represents the average squared difference between each value and the mean.
Range: Range is a simple measure of variability that calculates the difference between the maximum and minimum values in a dataset.
Interquartile Range (IQR): IQR measures the spread of data by calculating the range between the first quartile (25th percentile) and third quartile (75th percentile).
"Standard Deviation" appears in:
Subjects (1)
Study guides (22)
AP Statistics - 1.6 Describing the Distribution of a Quantitative Variable
AP Statistics - 1.7 Summary Statistics for a Quantitative Variable
AP Statistics - 2.5 Correlation
AP Statistics - 2.8 Least Squares Regression
AP Statistics - 3.5 Introduction to Experimental Design
AP Statistics - 3.7 Inference and Experiments
AP Statistics - 4.8 Mean and Standard Deviation of Random Variables
AP Statistics - 4.9 Combining Random Variables
AP Statistics - 4.11 Parameters for a Binomial Distribution
AP Statistics - 4.12 The Geometric Distribution
AP Statistics - 5.1 Introducing Statistics: Why Is My Sample Not Like Yours?
AP Statistics - 5.2 The Normal Distribution, Revisited
AP Statistics - 5.4 Biased and Unbiased Point Estimates
AP Statistics - 5.6 Sampling Distributions for Differences in Sample Proportions
AP Statistics - 5.8 Sampling Distributions for Differences in Sample Means
AP Statistics - 6.2 Constructing a Confidence Interval for a Population Proportion
AP Statistics - 7.5 Carrying Out a Test for a Population Mean
AP Statistics - 7.6 Confidence Intervals for the Difference of Two Means
AP Statistics - 8.1 Introducing Statistics: Are My Results Unexpected?
AP Statistics - 9.2 Confidence Intervals for the Slope of a Regression Model
AP Statistics - 9.4 Setting Up a Test for the Slope of a Regression Model
AP Statistics - 9.5 Carrying Out a Test for the Slope of a Regression Model
Additional resources (3)
Practice Questions (20+)
How does the sample size affect the standard deviation in statistical tests?
What is the role of the standard deviation in statistical inference?
What does the standard deviation of the residuals represent?
When constructing a confidence interval for a population mean, a larger standard deviation would result in:
To calculate the standard error of the mean, you divide the standard deviation of the sample by:
What is the effect of increasing the sample size on the standard deviation of a point estimate?
If the sample drawn from the population is of size 100 and the true population proportion is 0.38, what is the standard deviation of the sampling distribution for the sample proportion?
What step comes before square rooting when trying to find the overall standard deviation in a sample means for proportion differences?
In a sampling distribution for differences in sample proportions, what will happen to the standard deviation if the sample sizes are increased?
If you are only given the standard deviations for both samples in a proportion differences problem, how can you find the overall standard deviation?
Why do we divide the variances of each sample proportion by their sample size before finding the overall standard deviation?
Which version of standard deviation should you use for sample statistics?
What does a standard deviation of $10000 represent in a study of incomes?
How do you find the standard deviation of differences in sample means?
Which equation is the standard deviation for the distribution of the difference in sample means?
What is the standard deviation of a binomial random variable representing the number of successes in n independent trials with probability of success p?
In a binomial distribution, if the probability of success on each trial increases, what happens to the standard deviation?
What is the standard deviation of a geometric random variable?
In a statistics class, the scores on a midterm exam are normally distributed with a mean of 75 and a standard deviation of 10. What percentage of students scored below 80 on the exam?
How can the standard deviation of a discrete random variable's distribution be useful?
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