I can help analyze the contents of the image. It appears to contain a math problem involving the calculation of the mean (average) based on a frequency table and some additional tasks. Let's break it down step by step:

Part (a):

The table shows how the amount of money spent by a worker on Tuesday is distributed across different categories. For each category, the number of workers (frequency) is given, as well as the corresponding amount of money spent.

The task is to calculate the mean amount of money spent.

The formula for the mean is:

$\text{Mean} = \frac{\sum (f \times x)}{\sum f}$

Where:

• $f$ is the frequency (number of workers),
• $x$ is the amount of money spent.

Part (b):

This part asks to calculate a new mean if a new value is added to the dataset. Specifically, it asks what would happen if a worker spent $41.

The formula for the new mean is:

$\text{New Mean} = \frac{\sum (f \times x) + 41}{\sum f + 1}$

The hand-written calculations in the image suggest a specific value for the current mean of 8.79. Additionally, there are explanations in both (a) and (b) to clarify steps involved.

Would you like a detailed breakdown of each part of this problem, or should I help verify the steps shown in the image? Let me know if you need further clarification on any portion of the problem.

5 related questions:

1. How is a weighted mean different from a simple mean?
2. Can the median be more accurate in describing central tendency in such data?
3. How does adding outliers, such as the $41 in part (b), affect the mean?
4. Why do we need both the sum of frequencies and the sum of products in the mean formula?
5. What is the role of grouped data in calculating central tendencies like mean?

Tip:

Always check if your dataset has outliers, as they can significantly affect the mean, especially in small datasets.