Statistics Quiz
Test your understanding of standard deviation concepts
What does standard deviation measure?
The middle value in a data set
The spread or dispersion of data around the mean
The most frequently occurring value
The difference between the largest and smallest values
If all values in a data set are identical, what is the standard deviation?
1
It depends on the values
0
Undefined
What is the relationship between variance and standard deviation?
Variance is the square root of standard deviation
Standard deviation is the square root of variance
They are the same thing
Variance is double the standard deviation
When should you use sample standard deviation (s) instead of population standard deviation (σ)?
When working with a complete data set
When your data set has more than 100 values
When working with a subset of a larger population
When the data is normally distributed
In a normal distribution, approximately what percentage of data falls within one standard deviation of the mean?
50%
68%
95%
99.7%
Why does sample standard deviation divide by (n − 1) instead of n?
To make the calculation simpler
To correct for bias (Bessel's correction)
Because one data point is always an outlier
To account for measurement error
For the data set {2, 4, 4, 4, 5, 5, 7, 9}, what is the mean?
4
4.5
5
5.5
Which data set has the larger standard deviation?
A: {48, 49, 50, 51, 52}
B: {10, 30, 50, 70, 90}
They have the same standard deviation
Cannot be determined without calculation
What happens to the standard deviation if you add the same constant to every value in a data set?
It increases by that constant
It doubles
It stays the same
It decreases
What happens to the standard deviation if you multiply every value by 2?
It stays the same
It doubles
It quadruples
It is halved
What is a z-score?
The total number of standard deviations
The number of standard deviations a value is from the mean
The probability of a data point
The ratio of two standard deviations
Which of the following is NOT affected by outliers?
Mean
Standard deviation
Median
Variance
The coefficient of variation (CV) is useful for:
Finding the median of a data set
Comparing variability between data sets with different units or scales
Calculating the mode
Determining if data is normally distributed
In quality control, a process with a smaller standard deviation is generally considered:
Less efficient
More consistent and reliable
More variable
More expensive to maintain
What is the standard error of the mean?
The standard deviation of the original data
The error in calculating the mean
The standard deviation of the sampling distribution of the mean
The difference between the sample mean and population mean