All products in a factory are tested.

Each batch of products receives an overall score that shows how well it did in the tests. The higher the score, the better the batch of products.

This list shows the scores for all the batches from last month.

8.4 6.3 7.5 4.7
6.7 7.4 7.8 8.1
6.5 7.1 5.9 3.4
5.6 6.8 7.6 8.1

Tahir wants to report on the average score achieved last month. He wants the results to look as good as possible.

Should Tahir use the mean, median or mode?

Identify and compare the averages to find out which will give the best result.

To determine which average (mean, median, or mode) Tahir should use to make the scores appear as good as possible, let's calculate each type of average and compare them.

### 1. **Mean (Arithmetic Average)**:
The mean is calculated by adding up all the scores and dividing by the total number of scores.

The scores are:
\[ 8.4, 6.3, 7.5, 4.7, 6.7, 7.4, 7.8, 8.1, 6.5, 7.1, 5.9, 3.4, 5.6, 6.8, 7.6, 8.1 \]

The sum of the scores is:
\[ 8.4 + 6.3 + 7.5 + 4.7 + 6.7 + 7.4 + 7.8 + 8.1 + 6.5 + 7.1 + 5.9 + 3.4 + 5.6 + 6.8 + 7.6 + 8.1 = 107.9 \]

There are 16 scores, so the mean is:
\[
\text{Mean} = \frac{107.9}{16} \approx 6.74
\]

### 2. **Median**:
The median is the middle score when all the numbers are arranged in order. If there are an even number of scores, the median is the average of the two middle numbers.

First, let's arrange the scores in ascending order:
\[ 3.4, 4.7, 5.6, 5.9, 6.3, 6.5, 6.7, 6.8, 7.1, 7.4, 7.5, 7.6, 7.8, 8.1, 8.1, 8.4 \]

Since there are 16 scores, the median is the average of the 8th and 9th numbers:
\[
\text{Median} = \frac{6.8 + 7.1}{2} = \frac{13.9}{2} = 6.95
\]

### 3. **Mode**:
The mode is the number that appears most frequently. Here, the number 8.1 appears twice, while all other numbers appear only once. Therefore, the mode is:
\[
\text{Mode} = 8.1
\]

### Comparison:
- **Mean** = 6.74
- **Median** = 6.95
- **Mode** = 8.1

### Conclusion:
To make the scores look as good as possible, Tahir should use the **mode** because it is the highest of the three averages, giving the most favorable impression of the batch performance. Using the mode emphasizes that the most common score achieved is 8.1, which is higher than both the mean and the median.

Would you like further details on any part of this explanation?

---

Here are five related questions to extend your understanding:
1. How does the mean change if one low score (e.g., 3.4) is removed from the list?
2. What happens to the median if two more high scores are added to the data set?
3. Can a data set have more than one mode? If so, how would that affect the result?
4. How do outliers affect the mean compared to the median?
5. In what scenarios might the median be a better choice than the mean?

**Tip:** When choosing an average, consider whether the data contains outliers. Outliers can heavily skew the mean, but the median and mode are less sensitive to extreme values.

All products in a factory are tested. Each batch of products receives an overall score that shows how well it did in the tests. The higher the score, the better the batch of products. This list shows the scores for all the batches from last month: 8.4 6.3 7.5 4.7 6.7 7.4 7.8 8.1 6.5 7.1 5.9 3.4 5.6 6.8 7.6 8.1. Tahir wants to report on the average score achieved last month. He wants the results to look as good as possible. Should Tahir use the mean, median or mode? Identify and compare the averages to find out which will give the best result.

Discover how to compare the mean, median, and mode to determine which average gives the most favorable impression of last month's product test scores. Analyze a data set of batch scores from a factory and learn the statistical methods used to report the best possible result.

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