Weights of statistics students were obtained by a teacher as part of an experiment conducted for the class. The last digit of those weights are listed below. Construct a frequency distribution with 10 classes. Based on the​ distribution, do the weights appear to be reported or actually​ measured? What can be said about the accuracy of the​ results?
0

0

0

0

0

0

0

0

1

1

2

3

3

3

4

4

5

5

5

5

5

5

5

5

5

6

6

8

8

9

9

### Step 1: Organize the Data
The last digits of the students' weights are:

\[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 8, 8, 9, 9 \]

We will now create a frequency distribution with 10 classes, corresponding to the digits 0-9.

### Step 2: Construct the Frequency Distribution Table

| Last Digit | Frequency |
|------------|-----------|
| 0          | 8         |
| 1          | 2         |
| 2          | 1         |
| 3          | 3         |
| 4          | 2         |
| 5          | 9         |
| 6          | 2         |
| 7          | 0         |
| 8          | 2         |
| 9          | 2         |

### Step 3: Analyze the Distribution

1. **Observation of the Frequencies**:
   - The digit "5" has an unusually high frequency (9 occurrences), which is much higher compared to the other digits.
   - The digits "0" and "5" together account for a large portion of the data (17 out of 31 values), which suggests a pattern that could indicate rounding.

2. **Reported vs. Measured**:
   - If weights were actually measured, we would expect the digits to be more evenly distributed, as each last digit (0-9) should occur roughly the same number of times.
   - However, the high frequency of certain digits, particularly "0" and "5", suggests that the data may have been **reported** rather than **measured**. This likely indicates rounding, where individuals or the teacher rounded the weights to the nearest 5 or 0.

### Step 4: Conclusion on Accuracy

- The results likely **lack accuracy** because of this rounding effect. True measured data typically displays a more uniform distribution of last digits. Therefore, it is likely that some of the weights were not measured precisely but rather estimated or rounded.

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### Additional Questions:
1. Why would rounding occur frequently in reported weight data?
2. How would the distribution differ if the weights were measured with more precision?
3. Can we use this data to estimate any potential bias in the experiment?
4. How could we improve the data collection method to avoid rounding?
5. What statistical test could you apply to further investigate whether the data was reported or measured?

**Tip:** Always consider the potential for bias when data shows unusual patterns, such as a high frequency of rounded numbers.

Weights of statistics students were obtained by a teacher as part of an experiment conducted for the class. The last digit of those weights are listed below. Construct a frequency distribution with 10 classes. Based on the distribution, do the weights appear to be reported or actually measured? What can be said about the accuracy of the results?

This problem involves constructing a frequency distribution using the last digits of students' weights and analyzing the data for patterns indicating whether the weights were reported or actually measured. The solution includes key statistical concepts, such as frequency distribution and data accuracy analysis, suitable for high school students in Grades 10-12.

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