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Tina is a vet. She is doing a health check on some puppies. The table shows the weight of each puppy at two months old. At birth, the weights of these puppies had:
- a mode of 0.6 kg
- a range of 0.23 kg

Tina thinks that at two months old, the mode of the weights has increased by 4.5 kg and the weights are now more consistent. Is Tina correct?

\begin{tabular}{|c|c|}
\hline
Puppy & Weight (kg) \\
\hline
A & 4.70 \\
\hline
B & 4.90 \\
\hline
C & 5.15 \\
\hline
D & 4.70 \\
\hline
E & 4.90 \\
\hline
F & 4.80 \\
\hline
G & 4.75 \\
\hline
H & 4.90 \\
\hline
\end{tabular}

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Answer :

GinnyAnswer
Let's analyze the situation given in the problem. We need to determine if Tina's claims about the mode and consistency of the puppies' weights at two months old are correct.

### Given Data
- Weighed Puppies at Two Months Old:
- Puppy A: 4.70 kg
- Puppy B: 4.90 kg
- Puppy C: 5.15 kg
- Puppy D: 4.70 kg
- Puppy E: 4.90 kg
- Puppy F: 4.80 kg
- Puppy G: 4.75 kg
- Puppy H: 4.90 kg

- At Birth Data:
- Mode of weights: 0.6 kg
- Range of weights: 0.23 kg

### Tina's Claims
1. At two months old, the mode of the weights has increased by 4.5 kg.
2. The weights are now more consistent (i.e., the range is smaller).

### Calculations
1. Determine the Mode at Two Months Old:
The mode is the number that appears most frequently in a dataset.
- List of weights: [4.70, 4.90, 5.15, 4.70, 4.90, 4.80, 4.75, 4.90]
- Frequencies:
- 4.70 appears 2 times
- 4.90 appears 3 times
- 5.15 appears 1 time
- 4.80 appears 1 time
- 4.75 appears 1 time

Therefore, the mode is 4.90 kg.

2. Determine the Range at Two Months Old:
The range is the difference between the maximum and minimum values.
- Maximum weight: 5.15 kg
- Minimum weight: 4.70 kg
- Range = 5.15 kg - 4.70 kg = 0.45 kg

3. Verify Tina's Claims:
- Claim 1: Mode Increase
- Mode at birth: 0.6 kg
- Mode at two months: 4.90 kg
- Increase in mode: 4.90 kg - 0.6 kg = 4.30 kg
- Tina claimed an increase of 4.5 kg.
- Therefore, Tina’s claim about the mode is incorrect as the actual increase is 4.30 kg, not 4.5 kg.

- Claim 2: Weights More Consistent
- Range at birth: 0.23 kg
- Range at two months: 0.45 kg
- Tina claimed the weights at two months are more consistent.
- Since 0.45 kg > 0.23 kg, the range at two months is actually larger, indicating more variability.
- Therefore, Tina’s claim about the weights being more consistent is incorrect as the range has increased.

### Conclusion
Based on the analysis:
1. The mode of the weights has increased by 4.30 kg, not 4.5 kg.
2. The weights at two months are less consistent because the range increased from 0.23 kg to 0.45 kg.

Therefore, Tina is incorrect in both of her claims.