Based on the information provided about the temperatures of the children who visited a doctor's office, let's analyze each of the statements to determine which conclusions can be accurately drawn from the data set:
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The measures of center are the same.
This is not accurate. The measures of center include the mean (average) and the median. Given the distribution of temperatures, they are likely not the same. -
The interquartile range is 4.
To determine the interquartile range (IQR), we need to find the first quartile (Q1) and the third quartile (Q3). The temperatures listed are: 96, 97, 97, 98, 98, 98, 98, 98, 99, 99, 100. Here, Q1 (the median of the first half) is 98 and Q3 (the median of the second half) is also 99, giving us an IQR of 99 - 98 = 1. Therefore, this statement is not correct. -
There is little variability in the data.
Given that many of the temperatures are clustered around 98 degrees, and the measured temperatures are relatively close together, it is reasonable to say that there is little variability in the data. -
The average temperature is 98.
To calculate the average temperature: \[(1\cdot 96 + 2\cdot 97 + 5\cdot 98 + 2\cdot 99 + 1\cdot 100) / 11\] \[= (96 + 194 + 490 + 198 + 100) / 11 = 1078 / 11 \approx 98.00\] Therefore, the average temperature is indeed 98, so this statement is correct. -
The data is clustered around the mean.
Since many temperatures are close to 98 degrees (the mean), and there are more data points at that temperature value than at others, we can conclude that the data is clustered around the mean.
Based on this analysis, the correct conclusions are:
- There is little variability in the data.
- The average temperature is 98.
- The data is clustered around the mean.