Answer:
1. "It has no outliers": Since the lowest value is 1 and the highest value is 10, and there are no data points outside the whiskers of the box-and-whisker plot, we can confirm that there are no outliers. Therefore, this statement is true.
2. "50% of the data is between 6 and 10": The interquartile range (IQR) spans from 2 to 6, so 50% of the data is between these values. However, this statement contradicts the given information that the highest value is 10. Therefore, this statement is false.
3. "The IQR is 4": The interquartile range (IQR) is indeed calculated as the difference between the third quartile (Q3) and the first quartile (Q1), which is 6 - 2 = 4. So, this statement is true.
4. "The mean is 4": To determine if the mean is 4, we would need to calculate the mean of the dataset. However, we cannot directly infer the mean from the information provided about the quartiles and the range of values. Therefore, we cannot confirm the accuracy of this statement.
Based on the given details, statements 1 and 3 are correct, statement 2 is false, and statement 4 cannot be confirmed without further information or calculation.
