Final answer:
The data for index finger lengths are invalid due to the presence of extremely large values, such as 17.2 and 17.7 inches, which are very unlikely and suggest a measurement or recording error. Ensuring the accuracy and consistency of measurements is essential for valid data collection.
Step-by-step explanation:
The data you've provided about the lengths of students' index fingers is invalid due to the presence of some highly improbable values. The values of 17.2 inches and 17.7 inches are significantly outside the range of typical human index finger lengths. This suggests that there may have been an error in measurement or recording.
When collecting data for a statistical analysis, it is crucial to ensure the accuracy of the measurements. Instruments used for measuring, such as rulers or tape measures, should be checked for precision. If the ruler used in this scenario was not accurate or if there was a misinterpretation while reading the scale, it would lead to invalid data. In this case, the presence of two extremely large measurements suggests a likely error, as the average index finger length for an adult is usually between 2.7 and 3.9 inches.
An additional common issue that could render measurements invalid is the inconsistent rounding of numbers. Collecting data with a consistent level of precision is necessary when conducting an experiment where the results will be compared or aggregated. If measurements were rounded differently across samples, this could lead to flawed conclusions or an inaccurate representation of the data. However, in this case, the primary issue appears to be the incorrect measurements themselves.