To calculate whether the charity organizer's claim is true or false, we need to determine the mean amount of money collected this year using the given frequency and midpoint data.

Step 1: Compute the Total Money Collected

The formula for the mean is:

$\text{Mean} = \frac{\text{Total Money Collected}}{\text{Total Frequency}}$

To find the total money, we calculate the product of frequency and midpoint for each row and sum them up.

$\text{Total } f \times m = 35 + 60 + 150 + 35 + 90 = 370$ $\text{Total Frequency} = 7 + 4 + 6 + 1 + 2 = 20$

Step 2: Calculate the Mean

$\text{Mean} = \frac{\text{Total } f \times m}{\text{Total Frequency}} = \frac{370}{20} = 18.5$

Step 3: Compare with Last Year's Mean

Last year's mean was £14.85. This year's mean is £18.5, which is indeed more than £3 higher than last year.

Final Answer:

The organizer's claim is True.

Would you like a breakdown of how the midpoint values or totals were calculated? Let me know if you need more assistance!

Additional Questions:

1. What would the median amount be for the data given?
2. How would the mode of the money collected be calculated?
3. What is the range of the data in this dataset?
4. If one more person collected £45, how would the mean change?
5. How can we verify this calculation step by step without a calculator?

Tip: Always check the sum of frequencies to ensure the total matches the dataset before calculating the mean.