Question
The weight, in pounds, of each cat in an animal shelter is shown in the dot plot below.
The kitten that weighs 3 pounds was adopted today and is no longer in the shelter. Which of the following statements is not true about the distribution of the weight of the remaining cats?(1 point)
Responses
The range of the weight distribution decreased.
The range of the weight distribution decreased.
The mean of the weight distribution increased.
The mean of the weight distribution increased.
The median of the weight distribution increased.
The median of the weight distribution increased.
The standard deviation of the weight distribution decreased.
The kitten that weighs 3 pounds was adopted today and is no longer in the shelter. Which of the following statements is not true about the distribution of the weight of the remaining cats?(1 point)
Responses
The range of the weight distribution decreased.
The range of the weight distribution decreased.
The mean of the weight distribution increased.
The mean of the weight distribution increased.
The median of the weight distribution increased.
The median of the weight distribution increased.
The standard deviation of the weight distribution decreased.
Answers
GPT-4o mini
To evaluate the statements about the distribution of the weight of the remaining cats after the 3-pound kitten is adopted, we need to understand how the removal of that particular data point affects the various statistical measures.
1. **The range of the weight distribution decreased.**
- The range is calculated as the difference between the maximum and minimum weights. Since a 3-pound kitten is removed and is not the minimum weight (if there's a cat that weighs less than 3 pounds), the minimum will remain the same, and the maximum remains unchanged. In this case, the range will not decrease.
2. **The mean of the weight distribution increased.**
- Since a lower weight (3 pounds) is removed from the data, the total weight of the remaining cats decreases, which typically causes the mean to either decrease or stay the same. Hence, this statement is likely true.
3. **The median of the weight distribution increased.**
- If the 3-pound kitten was at the lower end of the weights, removing it could cause the median to either stay the same or increase, but it is not guaranteed to increase unless the middle values change. However, we cannot say for sure that the median must increase.
4. **The standard deviation of the weight distribution decreased.**
- The standard deviation measures how spread out the weights are. Removing a kitten that weighs less than the mean could result in the standard deviation increasing, as the remaining values may become more clustered around the new mean.
Thus, the statement that **"the median of the weight distribution increased"** is not necessarily true, especially if the 3-pound kitten was not at the median position originally.
Therefore, the statement that is not true is:
**The median of the weight distribution increased.**
1. **The range of the weight distribution decreased.**
- The range is calculated as the difference between the maximum and minimum weights. Since a 3-pound kitten is removed and is not the minimum weight (if there's a cat that weighs less than 3 pounds), the minimum will remain the same, and the maximum remains unchanged. In this case, the range will not decrease.
2. **The mean of the weight distribution increased.**
- Since a lower weight (3 pounds) is removed from the data, the total weight of the remaining cats decreases, which typically causes the mean to either decrease or stay the same. Hence, this statement is likely true.
3. **The median of the weight distribution increased.**
- If the 3-pound kitten was at the lower end of the weights, removing it could cause the median to either stay the same or increase, but it is not guaranteed to increase unless the middle values change. However, we cannot say for sure that the median must increase.
4. **The standard deviation of the weight distribution decreased.**
- The standard deviation measures how spread out the weights are. Removing a kitten that weighs less than the mean could result in the standard deviation increasing, as the remaining values may become more clustered around the new mean.
Thus, the statement that **"the median of the weight distribution increased"** is not necessarily true, especially if the 3-pound kitten was not at the median position originally.
Therefore, the statement that is not true is:
**The median of the weight distribution increased.**