Mean & Standard Deviation

What is standard deviation?

• A measure of central tendency in a data set.

• A measure of the amount of variation or dispersion in a set of values.

• A method for calculating the mean of a data set.

• A technique for visualizing data distributions.

What is the relationship between variance and standard deviation?

• Standard deviation is the square root of variance.

• Variance is the square root of standard deviation.

• Standard deviation and variance are the same thing.

• Variance is always greater than standard deviation.

What is the mean of a set of numbers?

• The mean is the sum of all numbers in the set.

• The mean is the average of a set of numbers, calculated by adding all the numbers together and dividing by the count of numbers.

• The mean is the largest number in the set.

• The mean is the smallest number in the set.

Given the data set {5, 10, 7, 12, 0, 20, 15, 22, 8, 2}, what is the standard deviation?

• 5.34

• 6.89

• 7.45

• 8.12

How do you find the variance of a data set?

• 1. Find the mean, then subtract the mean from each data point and square the result. Finally, find the average of those squared differences.

• 2. Add all data points together and divide by the number of data points.

• 3. Find the median of the data set and use it to calculate the variance.

• 4. Calculate the range of the data set and divide by the number of data points.

What is variance in statistics?

• Variance is the average of the squared differences from the mean, and it is the square of the standard deviation.

• Variance is the sum of all data points divided by the number of data points.

• Variance is a measure of the central tendency of a dataset.

• Variance is the difference between the highest and lowest values in a dataset.

What is the formula for population standard deviation?

• σ = √(Σ(xi - μ)² / N), where μ is the population mean and N is the number of data points.

• σ = Σ(xi - μ) / N, where μ is the population mean and N is the number of data points.

• σ = √(Σ(xi - μ) / N), where μ is the population mean and N is the number of data points.

• σ = (Σ(xi - μ)²) / N², where μ is the population mean and N is the number of data points.

What does a low standard deviation indicate about a data set?

• A low standard deviation indicates that the data points tend to be close to the mean, showing less variability.

• A low standard deviation indicates that the data points are widely spread out from the mean.

• A low standard deviation indicates that the data set has a high range of values.

• A low standard deviation indicates that the data points are all identical.

What does a high standard deviation indicate about a data set?

• A high standard deviation indicates that the data points are spread out over a wider range of values, showing more variability.

• A high standard deviation indicates that the data points are clustered closely around the mean.

• A high standard deviation indicates that the data set has a low level of variability.

• A high standard deviation indicates that the data points are all identical.

What is the formula for sample standard deviation?

• s = √(Σ(xi - x̄)² / n)

• s = √(Σ(xi - x̄)² / (n + 1))

• s = √(Σ(xi - x̄)² / (n - 1))

• s = Σ(xi - x̄) / n