The distribution of test scores for a class are represented by the dot plot below. If another test score of 80 was later added to the data set, which of the following is not true about the data set when the new score is included? Responses The interquartile range increases. The interquartile range increases. The Q3 increases. The Q3 increases. The standard deviation increases. The standard deviation increases. The mean stays the same.
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GPT-4o mini
To analyze the impact of adding a new test score of 80 to the data set, we can consider the following points:
1. **Interquartile Range (IQR)**: The interquartile range (IQR) is calculated as Q3 - Q1. Adding a score of 80 may or may not change Q1 and Q3 depending on the existing scores. If the new score is within the 1st or 3rd quartile range, it could potentially increase Q3, particularly if Q3 is just greater than 80. Therefore, it is likely that the IQR increases, but we should be careful about stating this as a definitive outcome.
2. **Q3**: Q3 is likely to increase if the existing Q3 is less than 80, as adding a score of 80 would push the upper end of the data set to consider new values.
3. **Standard Deviation**: The standard deviation measures how much the scores deviate from the mean. Adding a score of 80 could either increase or decrease the standard deviation depending on how it affects the overall distribution of scores relative to the mean. If the existing scores are much higher than 80, it is likely to increase, but again, this isn't guaranteed without specific data.
4. **Mean**: The mean will definitely change because a new score is added. The original mean is the total of all scores divided by the number of scores. Adding an additional score generally affects this calculation.
With all of this information, the statement that is **not true** about the data set when the new score is included is:
**The mean stays the same.**
Adding a score will typically affect the mean, so that statement is false.
1. **Interquartile Range (IQR)**: The interquartile range (IQR) is calculated as Q3 - Q1. Adding a score of 80 may or may not change Q1 and Q3 depending on the existing scores. If the new score is within the 1st or 3rd quartile range, it could potentially increase Q3, particularly if Q3 is just greater than 80. Therefore, it is likely that the IQR increases, but we should be careful about stating this as a definitive outcome.
2. **Q3**: Q3 is likely to increase if the existing Q3 is less than 80, as adding a score of 80 would push the upper end of the data set to consider new values.
3. **Standard Deviation**: The standard deviation measures how much the scores deviate from the mean. Adding a score of 80 could either increase or decrease the standard deviation depending on how it affects the overall distribution of scores relative to the mean. If the existing scores are much higher than 80, it is likely to increase, but again, this isn't guaranteed without specific data.
4. **Mean**: The mean will definitely change because a new score is added. The original mean is the total of all scores divided by the number of scores. Adding an additional score generally affects this calculation.
With all of this information, the statement that is **not true** about the data set when the new score is included is:
**The mean stays the same.**
Adding a score will typically affect the mean, so that statement is false.