true or false
The value for the standard deviation cannot be larger than the value for the range.
false
True, ±3 SD < range.
True. The value for the standard deviation cannot be larger than the value for the range. The standard deviation is a measure of the spread or dispersion of a set of data points around the mean, while the range is the difference between the maximum and minimum values in a data set.
To determine if this statement is true or false, you can calculate the standard deviation and the range for a set of data and compare their values. Here are the steps to do that:
1. Collect a set of data points for which you want to calculate the standard deviation and range.
2. Find the mean of the data set by summing all the values and dividing by the total number of data points.
3. Calculate the standard deviation by finding the square root of the variance, which is the average of the squared differences between each data point and the mean.
- Calculate the difference between each data point and the mean.
- Square each difference.
- Calculate the average of the squared differences.
- Take the square root of the average to get the standard deviation.
4. Calculate the range by subtracting the minimum value from the maximum value in the data set.
5. Compare the values of the standard deviation and the range. If the standard deviation is larger than the range, then the statement is false. If the standard deviation is smaller or equal to the range, then the statement is true.