Question to test your Frequency Distributions knowledge

Question

The heights of students were collected as part of a high school health survey. Below are the last digits of heights (in cm) from a randomly selected sample of $50$ students. Create a frequency distribution with 10 classes and use it to answer the following questions.
i. Do the recorded heights seem to be self-reported or directly measured?
ii. Is there a noticeable gap in the frequency distribution? If so, what could be the possible reason for it?
iii. What can be inferred about the accuracy of the recorded data?
Last Digits Data Set:
$2 comma 7 comma 5 comma 3 comma 9 comma 8 comma 5 comma 0 comma 4 comma 1 comma 6 comma 3 comma 7 comma 2 comma 9 comma 8 comma 5 comma 1 comma 4 comma 6 comma 2 comma 7 comma 5 comma 3 comma 9 comma 8 comma 5 comma 0 comma 4 comma 1 comma 6 comma 3 comma 7 comma 2 comma 9 comma 8 comma 5 comma 1 comma 4 comma 6 comma 2 comma 7 comma 5 comma 3 comma 9 comma 8 comma 5 comma 0 comma 4 comma 1$

Accepted Answer

i. The data appears to be directly measured because the distribution of last digits is fairly uniform.

ii. No, the distribution is fairly uniform, meaning there are no significant gaps.

iii. The data appears accurate because the digits are evenly distributed, suggesting measured values.

Answer

i. The data appears to be self-reported because some digits appear more frequently.

ii. Yes, there is a noticeable gap, which suggests that students avoided certain digits when reporting their heights.

iii. The data is likely inaccurate because heights should only end in certain digits.

Answer

i. The data appears to be directly measured because the distribution of last digits is fairly uniform.

ii. No, the distribution is fairly uniform, meaning there are no significant gaps.

iii. The data is inaccurate because the last digits should always be the same.

Answer

i. The data is self-reported because all numbers occur with exactly the same frequency.

ii. No, but the gaps would be clearer if we used more than $10$ classes.

iii. The data appear accurate because the digits are evenly distributed, suggesting measured values.