To determine which statement is not true after the adoption of the 3-pound kitten, we can analyze how each measure of central tendency or variability is affected.
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Mean: The mean is the average weight of all cats. Removing the 3-pound cat would generally increase the mean because it’s likely lower than the mean of the remaining weights.
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Standard Deviation: The standard deviation measures the spread of the weights. If a cat with a weight less than or equal to the mean (in this case, 3 pounds) is removed, the remaining weights will tend to be further from the mean, which usually increases standard deviation rather than decreases it.
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Range: The range is the difference between the maximum and minimum weights. Removing the 3-pound cat (if it was the minimum) could decrease the minimum weight if there are no other weights lower than 3 pounds. However, if there are heavier cats, the range will not necessarily decrease; it depends on the minimum weight of the remaining cats.
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Median: The median is the middle value when the weights are ordered. Removing the 3-pound cat would not generally increase the median, as it is likely located at the lower end of the distribution.
Given these analyses, the statement that is not true is:
"The standard deviation of the weight distribution decreased."
This statement is not true because removing a low weight generally increases the standard deviation, as the distribution becomes more spread out.