


Here's a business-related dataset focused on monthly customer orders for two branches, Branch A and Branch B, of a retail company. The students will fill in some fields using three-digit numbers based on their personal data.

Month

Number	

Branch A's Orders (Units)	

Branch B's Orders (Units)Month

Number	

Branch A's Orders (Units)	

Branch B's Orders (Units)Month

Number	

Branch A's Orders (Units)	

Branch B's Orders (Units)

1	345	289



2	125	105



3	412	178

4	368	450



5	60	

310



6	838	222



For any datasets, which value impacts on the mean values? Identify whether the above data set has such values. Compare your results for both data sets.




To determine the impact of individual values on the mean (average) of a dataset, we need to first calculate the mean for each branch (Branch A and Branch B) using the provided data. After calculating the means, we can assess if any specific values stand out as unusually high or low (outliers), which might significantly affect the mean.

### Steps to Solve:

1. **Calculate the mean** for Branch A's and Branch B's orders.
2. **Identify potential outliers** that may heavily influence the means.

### Dataset:

| Month Number | Branch A's Orders (Units) | Branch B's Orders (Units) |
|--------------|---------------------------|---------------------------|
| 1            | 345                       | 289                       |
| 2            | 125                       | 105                       |
| 3            | 412                       | 178                       |
| 4            | 368                       | 450                       |
| 5            | 60                        | 310                       |
| 6            | 838                       | 222                       |

---

### Step 1: Calculating the Mean

- **For Branch A**:
  
  The values provided are: \( 345, 125, 412, 368, 60, 838 \)

  To calculate the mean:
  \[
  \text{Mean for Branch A} = \frac{345 + 125 + 412 + 368 + 60 + 838}{6} = \frac{2148}{6} = 358
  \]

- **For Branch B**:
  
  The values provided are: \( 289, 105, 178, 450, 310, 222 \)

  To calculate the mean:
  \[
  \text{Mean for Branch B} = \frac{289 + 105 + 178 + 450 + 310 + 222}{6} = \frac{1554}{6} = 259
  \]

---

### Step 2: Identifying Outliers

- **Branch A**:
  - The average is \( 358 \), but the value \( 838 \) is significantly larger than the other values. This could be an outlier that might skew the mean upwards. Without \( 838 \), the mean would have been:
    \[
    \frac{345 + 125 + 412 + 368 + 60}{5} = \frac{1310}{5} = 262
    \]
    This is much lower than the original mean of \( 358 \), showing that \( 838 \) strongly impacts the mean.

- **Branch B**:
  - The average is \( 259 \), and while the values \( 450 \) and \( 105 \) are on the higher and lower ends, they don’t seem as extreme as \( 838 \) in Branch A. Therefore, the impact of any one value on the mean of Branch B is less significant.

### Step 3: Conclusion

- **Branch A's mean** is heavily impacted by the high value of \( 838 \), which raises the mean significantly.
- **Branch B's mean** appears more balanced, with no extreme outliers that drastically shift the average.

---

Would you like more detailed analysis on these findings, or have any specific questions?

Here are 5 questions that could further expand on this information:
1. How would the median help identify outliers compared to the mean in this dataset?
2. What impact does removing the outlier have on Branch A's overall performance analysis?
3. How do outliers typically affect business decisions in a retail setting?
4. Could the standard deviation provide more insights into the variability of these datasets?
5. What would happen to the mean if all data were rounded to the nearest hundred?

**Tip:** Outliers can significantly affect the mean, but the median is often more resistant to these extreme values, making it a useful measure when dealing with skewed data.

Here's a business-related dataset focused on monthly customer orders for two branches, Branch A and Branch B, of a retail company. The students will fill in some fields using three-digit numbers based on their personal data. Month Number Branch A's Orders (Units) Branch B's Orders (Units) 1 345 289 2 125 105 3 412 178 4 368 450 5 60 310 6 838 222. For any datasets, which value impacts on the mean values? Identify whether the above dataset has such values. Compare your results for both datasets.

Explore how outliers in the monthly customer orders of Branch A and Branch B affect the mean values. Learn to calculate the mean, identify outliers, and compare the results using a real business dataset. This example highlights the significance of data analysis for Grades 10-12.

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