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Sagot :
One description that is not correct as regards South Carolina counties is C. The distribution is skewed to the right.
What does the stemplot show?
The distribution is skewed to the left, not to the right. This means that there are more counties with smaller areas than with larger areas, and the tail of the distribution extends to the left.
To see this, we can look at the stemplot and notice that the stems with higher values (such as 11, 12, and 13) have fewer leaves than the stems with lower values (such as 3, 4, and 5). We can also calculate the mean and the median of the data and compare them. The mean is 610.87 mi2 and the median is 516.5 mi2. The mean is larger than the median, which is another indication of left skewness.
The other three options are correct descriptions of the distribution of area for the 46 South Carolina counties.
- A. The distribution has one outlier, which is the county with an area of 1,358 mi2.
This is a correct description of the distribution of area for the 46 South Carolina counties. An outlier is a data value that is much higher or lower than the rest of the data. The county with an area of 1,358 mi2 is much higher than the other counties, and it is the only county with a stem of 13. We can also use the 1.5IQR rule to identify outliers. The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1) of the data. The 1.5IQR rule states that any data value that is more than 1.5IQR above Q3 or below Q1 is an outlier. In this case, Q1 is 392.5 mi2 and Q3 is 757.5 mi2, so the IQR is 365 mi2. 1.5IQR is 547.5 mi2, so any county with an area more than 1,305 mi2 or less than -155 mi2 is an outlier. The county with an area of 1,358 mi2 is the only one that satisfies this condition.
- B. The distribution is roughly symmetric around 500 mi2.
This is a correct description of the distribution of area for the 46 South Carolina counties, if we ignore the outlier. Symmetry means that the left and right halves of the distribution are approximately mirror images of each other. To check for symmetry, we can look at the stemplot and compare the stems on either side of 500 mi2. We can see that the stems of 3, 4, and 5 have roughly the same number of leaves as the stems of 6, 7, and 8, and the leaves are similarly spread out. We can also use the mean and the median to check for symmetry. If the distribution is symmetric, the mean and the median should be close to each other. In this case, the mean is 610.87 mi2 and the median is 516.5 mi2, which are not very far apart. However, the mean is affected by the outlier, which pulls it to the right. If we exclude the outlier, the mean is 584.8 mi2, which is closer to the median.
- D. The distribution has a range of 1,310 mi2.
This is a correct description of the distribution of area for the 46 South Carolina counties. The range is the difference between the maximum and the minimum values of the data. The maximum value is 1,358 mi2 and the minimum value is 48 mi2, so the range is 1,358 - 48 = 1,310 mi2."
Find out more on stemplots at https://brainly.com/question/29433270
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Options for this question include:
- A. The distribution has one outlier, which is the county with an area of 1,358 mi2.
- B. The distribution is roughly symmetric around 500 mi2.
- C. The distribution is skewed to the right.
- D. The distribution has a range of 1,310 mi2.
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