Answer :
To analyze the donations data from the two years provided, we will investigate the mean donations and the range. The mean will help us determine which year had more money donated on average, while the range will help us understand the consistency of the donations.
Here is the data again for clarity:
[tex]\[ \begin{tabular}{|l|l|l|} \hline & Mean & Range \\ \hline Year 1 & £527 & £328 \\ \hline Year 2 & £572 & £574 \\ \hline \end{tabular} \][/tex]
Step-by-step solution:
### Step 1: Compare the Mean Donations
The mean donation value indicates the average amount donated in each year:
- Mean for Year 1: £527
- Mean for Year 2: £572
To determine which year had more money donated on average, we compare the mean values:
- Since £527 (mean for Year 1) is less than £572 (mean for Year 2), we can conclude that more money was donated in Year 2 on average.
Thus, the statement "More money was donated in Year 1 than in Year 2" is FALSE.
### Step 2: Compare the Consistency of Donations
Consistency in donations can be measured by looking at the range of donations. A smaller range indicates more consistency, as it suggests less variability in the data:
- Range for Year 1: £328
- Range for Year 2: £574
To determine which year had more consistent donations, we compare these ranges:
- Since £328 (range for Year 1) is less than £574 (range for Year 2), we can conclude that the donations in Year 1 were more consistent because the smaller range indicates less variability.
Thus, the statement "The amounts donated in Year 1 were more consistent than in Year 2" is TRUE.
### Step 3: Compare the Inconsistency of Donations
To check if the donations in Year 1 were less consistent than in Year 2, we again rely on the range values. A larger range indicates less consistency:
- Range for Year 1: £328
- Range for Year 2: £574
Here, since £328 (range for Year 1) is less than £574 (range for Year 2), it indicates that Year 1 had a smaller spread and therefore was more consistent. Thus, the amounts donated in Year 1 were not less consistent than in Year 2.
Thus, the statement "The amounts donated in Year 1 were less consistent than in Year 2" is FALSE.
### Summary of Statements:
1. More money was donated in Year 1 than in Year 2: FALSE
2. The amounts donated in Year 1 were more consistent than Year 2: TRUE
3. The amounts donated in Year 1 were less consistent than Year 2: FALSE
Based on our analysis, these are the correct conclusions based on the given data.
Here is the data again for clarity:
[tex]\[ \begin{tabular}{|l|l|l|} \hline & Mean & Range \\ \hline Year 1 & £527 & £328 \\ \hline Year 2 & £572 & £574 \\ \hline \end{tabular} \][/tex]
Step-by-step solution:
### Step 1: Compare the Mean Donations
The mean donation value indicates the average amount donated in each year:
- Mean for Year 1: £527
- Mean for Year 2: £572
To determine which year had more money donated on average, we compare the mean values:
- Since £527 (mean for Year 1) is less than £572 (mean for Year 2), we can conclude that more money was donated in Year 2 on average.
Thus, the statement "More money was donated in Year 1 than in Year 2" is FALSE.
### Step 2: Compare the Consistency of Donations
Consistency in donations can be measured by looking at the range of donations. A smaller range indicates more consistency, as it suggests less variability in the data:
- Range for Year 1: £328
- Range for Year 2: £574
To determine which year had more consistent donations, we compare these ranges:
- Since £328 (range for Year 1) is less than £574 (range for Year 2), we can conclude that the donations in Year 1 were more consistent because the smaller range indicates less variability.
Thus, the statement "The amounts donated in Year 1 were more consistent than in Year 2" is TRUE.
### Step 3: Compare the Inconsistency of Donations
To check if the donations in Year 1 were less consistent than in Year 2, we again rely on the range values. A larger range indicates less consistency:
- Range for Year 1: £328
- Range for Year 2: £574
Here, since £328 (range for Year 1) is less than £574 (range for Year 2), it indicates that Year 1 had a smaller spread and therefore was more consistent. Thus, the amounts donated in Year 1 were not less consistent than in Year 2.
Thus, the statement "The amounts donated in Year 1 were less consistent than in Year 2" is FALSE.
### Summary of Statements:
1. More money was donated in Year 1 than in Year 2: FALSE
2. The amounts donated in Year 1 were more consistent than Year 2: TRUE
3. The amounts donated in Year 1 were less consistent than Year 2: FALSE
Based on our analysis, these are the correct conclusions based on the given data.
