To calculate the difference between the mean values of two data sets, follow these steps:
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Calculate the Mean of Each Data Set:
- For each data set, sum all the values together.
- Divide the sum by the number of values (n) in that data set.
The formula for the mean (\( \bar{x} \)) is: \[ \bar{x} = \frac{\sum_{i=1}^{n} x_i}{n} \] where \( x_i \) represents each value in the data set.
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Calculate the Difference Between the Means:
- Once you have the mean of each data set, subtract the mean of the second data set from the mean of the first data set.
The formula for the difference in means is: \[ \text{Difference} = \bar{x}_1 - \bar{x}_2 \] where \( \bar{x}_1 \) is the mean of the first data set and \( \bar{x}_2 \) is the mean of the second data set.
Example:
Suppose you have the following two data sets:
- Data Set 1: 4, 6, 8, 10
- Data Set 2: 5, 7, 9, 11
Step 1: Calculate the Means
For Data Set 1:
- Sum: \( 4 + 6 + 8 + 10 = 28 \)
- Number of values: \( 4 \)
- Mean: \( \bar{x}_1 = \frac{28}{4} = 7 \)
For Data Set 2:
- Sum: \( 5 + 7 + 9 + 11 = 32 \)
- Number of values: \( 4 \)
- Mean: \( \bar{x}_2 = \frac{32}{4} = 8 \)
Step 2: Calculate the Difference Between the Means
- Difference: \( \text{Difference} = \bar{x}_1 - \bar{x}_2 = 7 - 8 = -1 \)
So, the difference between the mean values of the two data sets is \(-1\).