Calculate Sum of Squares (SS) for Data Set

Which participant score from the previous SS calculation contributes the greatest amount of variability to the SS? The participant score from the previous SS calculation that contributes the greatest amount of variability to the SS is 34. This can be determined by looking at the squared difference of each value from the mean. We see that the squared difference of 34 is much larger than the other values, indicating that this value is further away from the mean and contributes the most to the variability of the data set.

Understanding Sum of Squares (SS) Calculation

Sum of Squares (SS) measures variability in a data set by calculating the sum of squared differences between individual values and the mean. It helps in understanding how spread out the values are from the mean, providing insights into the overall variability of the data.

Calculating SS for the Data Set

To calculate SS for the data set 12, 19, 34, 11, 7, 22, we first need to find the mean of the data set. The mean is calculated by adding up all the values and dividing by the total number of values.

Mean = (12 + 19 + 34 + 11 + 7 + 22) / 6 = 105 / 6 = 17.5

Next, we calculate the squared difference for each value from the mean:

  • (12 - 17.5)^2 = 30.25
  • (19 - 17.5)^2 = 2.25
  • (34 - 17.5)^2 = 289
  • (11 - 17.5)^2 = 42.25
  • (7 - 17.5)^2 = 110.25
  • (22 - 17.5)^2 = 20.25

Summing up these squared differences gives us the SS value:

SS = 30.25 + 2.25 + 289 + 42.25 + 110.25 + 20.25 = 479.3125

Therefore, the SS for the data set 12, 19, 34, 11, 7, 22 is 479.3125. The participant score of 34 contributes the most to the variability of the data set, indicating that it is further away from the mean compared to other values.

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