An illustration shows two sets of dot plots. One is titled Weight in Pounds, Cats and the other is Weight in Pounds, Small Dogs. The plots are shown as an abacus-like representation with dots in a vertical row over each number on a number line. For Cats, a number line with arrows on both ends ranges from 9 to 13 in increments of 1. There is 1 dot above 9, 2 dots above 10, 4 dots above 11, 2 dots above 12, and one dot above 13.
For Small Dogs, a number line with arrows on both ends ranges from 8 to 15 in increments of 1. There is 1 dot above 8, 2 dots above 9, 4 dots above 10, 2 dots above 11, 2 dots above 12, 2 dots above 13, 1 dot above 14, and 1 dot above 15.
The dot plots show the weights of randomly selected cats and small dogs in different households. Based on an informal assessment of the visual overlap of these distributions, which animal has the least variability in their weights? Why?
Small dogs have the least variability in their weights. This is because the dots for small dogs are clustered tightly around the middle of the number line, indicating that most small dogs in the sample have weights close to the average. In contrast, the dots for cats are more spread out, indicating greater variability in cat weights.
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a Small dogs, because the range of their weights is less than that of cats.
b Cats, because the range of their weights is greater than that of small dogs.
c Small dogs, because the range of their weights is greater than that of cats.
d Cats, because the range of their weights is less than that of small dogs.
Based on the given information, the correct answer is:
d Cats, because the range of their weights is less than that of small dogs.
Please note that the answer choices were not provided initially.
To determine which animal has the least variability in their weights based on the dot plots, we need to look at the spread or dispersion of the dots on each plot.
In the Cat dot plot, the data ranges from 9 to 13, and we have 1 dot above 9, 2 dots above 10, 4 dots above 11, 2 dots above 12, and 1 dot above 13. We can observe that the majority of the dots are centered around 11, and there are no extreme outliers.
In the Small Dog dot plot, the data ranges from 8 to 15, and we have 1 dot above 8, 2 dots above 9, 4 dots above 10, 2 dots above 11, 2 dots above 12, 2 dots above 13, 1 dot above 14, and 1 dot above 15. Similar to the Cat dot plot, the dots are centered around 11, and there are no extreme outliers.
From this visual analysis, we can conclude that both the Cat and Small Dog dot plots have similar shape and central tendencies. However, when considering variability, we see that the Small Dog dot plot has dots spread out across a wider range of values compared to the Cat dot plot. The presence of dots above 14 and 15 indicates some higher weights in small dogs, which are not present in the Cat dot plot.
Therefore, based on this informal assessment, the Small Dogs have more variability in their weights compared to Cats, as indicated by the wider spread of dots in the Small Dog dot plot.