QuestionEileen has a data set with 12 values and a standard deviation of 0. What must be true? Select all that apply.
Studdy Solution
STEP 1
Assumptions1. The data set has12 values. . The standard deviation of the data set is0.
STEP 2
The 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 (average) value of the set, while a high standard deviation means that the values are spread out over a wider range.
STEP 3
If the standard deviation is0, it means there is no variation in the data set. All the values in the data set are the same.
STEP 4
Therefore, all values in the data set are equal.
STEP 5
If all values in the data set are equal, then the mean and median of the set are also equal. This is because the mean is the average of all the values, and the median is the middle value when the values are arranged in numerical order. If all the values are the same, then the mean and median are also the same.
STEP 6
If all values in the data set are equal, then the range of the set is equal to zero. This is because the range is calculated as the difference between the highest and lowest values in the set. If all the values are the same, then the highest and lowest values are also the same, and their difference is zero.
STEP 7
If all values in the data set are equal, then the spread of the set is not greater than its range. The spread of a data set is a measure of how much the data varies, and can be measured in several ways, including the range, interquartile range, and standard deviation. If all the values are the same, then there is no variation in the data, and the spread is zero, which is not greater than the range.
STEP 8
If all values in the data set are equal, then the set does not have repeated values and pairs of values are not equally placed on opposite sides of the mean. This is because there is only one unique value in the set, and it is not possible to have pairs of values on opposite sides of the mean.
So, the statements that must be true of the data set are- The mean and median of the set are equal.
- All values in the data set are equal.
- The range of the set is equal to zero.
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