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Answer :
To determine which data set has data values that are more widely spread out, we look at the sum of squares for each data set. The sum of squares is a measure of the total variability or dispersion of values in a data set. A higher sum of squares indicates that the data values are more spread out from their mean.
Here’s a step-by-step explanation:
1. Understand the Sum of Squares:
- The sum of squares is calculated by taking each data point in a data set, subtracting the mean of the data set from each data point (to find the deviation from the mean), squaring each of these differences, and then adding them all up.
- A larger sum of squares suggests a greater spread of data points around the mean.
2. Compare Data Set A and Data Set B:
- Data Set A has a sum of squares of 97.
- Data Set B has a sum of squares of 197.
3. Interpret the Values:
- Since Data Set B has a sum of squares of 197, which is larger than Data Set A's sum of squares of 97, this implies that Data Set B has more variability.
- This means the values in Data Set B are more widely spread out from the mean compared to Data Set A.
4. Conclusion:
- Therefore, Data Set B is the one where the data values are more widely spread out. The correct option is:
"Data set B, because a sum of squares of 197 is bigger than a sum of squares of 97."
This step-by-step reasoning shows how we can assess variability in data sets using the sum of squares and why Data Set B exhibits more spread in its data values.
Here’s a step-by-step explanation:
1. Understand the Sum of Squares:
- The sum of squares is calculated by taking each data point in a data set, subtracting the mean of the data set from each data point (to find the deviation from the mean), squaring each of these differences, and then adding them all up.
- A larger sum of squares suggests a greater spread of data points around the mean.
2. Compare Data Set A and Data Set B:
- Data Set A has a sum of squares of 97.
- Data Set B has a sum of squares of 197.
3. Interpret the Values:
- Since Data Set B has a sum of squares of 197, which is larger than Data Set A's sum of squares of 97, this implies that Data Set B has more variability.
- This means the values in Data Set B are more widely spread out from the mean compared to Data Set A.
4. Conclusion:
- Therefore, Data Set B is the one where the data values are more widely spread out. The correct option is:
"Data set B, because a sum of squares of 197 is bigger than a sum of squares of 97."
This step-by-step reasoning shows how we can assess variability in data sets using the sum of squares and why Data Set B exhibits more spread in its data values.
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