Mean and Standard deviation

Front

What is the mean?

Back

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

Front

What is the median?

Back

The median is the middle number in a sorted list of numbers. If there is an even number of observations, the median is the average of the two middle numbers.

Front

What is standard deviation?

Back

Standard deviation is a measure of the amount of variation or dispersion in a set of values. A low standard deviation means that the values tend to be close to the mean, while a high standard deviation means that the values are spread out over a wider range.

Front

How do you calculate the mean of a set of numbers?

Back

To calculate the mean, add all the numbers together and divide by the total count of numbers.

Front

What is the formula for standard deviation?

Back

The formula for standard deviation is: \( \sigma = \sqrt{\frac{\sum (x - \mu)^2}{N}} \) where \( \mu \) is the mean, \( x \) represents each value, and \( N \) is the number of values.

Front

If the grades are 50, 70, 88, 70, and 88, what is the mean?

Back

The mean is 73.

Front

If the grades are 100, 96, 96, and 100, what is the mean?

Back

The mean is 98.

Front

What does a standard deviation of 0 indicate?

Back

A standard deviation of 0 indicates that all values in the dataset are identical and there is no variation.

Front

What is the range of a dataset?

Back

The range is the difference between the highest and lowest values in a dataset.

Front

How does the mean differ from the median?

Back

The mean is affected by extreme values (outliers), while the median is not, making the median a better measure of central tendency for skewed distributions.