Suppose, you are to take the measurements of the mass of a 50.0-gram standard sample with a weighing balance. You get values of 47.5, 47.6, 47.5 and 47.7 grams with weighing machine-1 and 49.8, 50.5, 51.0, 49.6 with machine-2, then
(A) Machine 1 is more accurate and less precise
(B) Machine 2 is more assurate and less precise
(C) Machine 1 is less accurate and more precise
(D) Machine 2 is less accurate and more percise Select correct alternative.

Options

A. A,B
B. B,C
C. A,D
D. C,D

Answer

To solve the problem, we need to analyze the measurements obtained from both weighing machines in terms of accuracy and precision.

### Step 1: Understand the Definitions
- **Accuracy** refers to how close a measured value is to the true value (in this case, 50.0 grams).
- **Precision** refers to how close the measured values are to each other, regardless of how close they are to the true value.

### Step 2: Analyze Measurements from Machine 1
The measurements from Machine 1 are:
- 47.5 grams
- 47.6 grams
- 47.5 grams
- 47.7 grams

**Calculate the average:**
\[ \text{Average} = \frac{(47.5 + 47.6 + 47.5 + 47.7)}{4} = \frac{190.3}{4} = 47.575 \text{ grams} \]

**Determine the range:**
- Minimum = 47.5 grams
- Maximum = 47.7 grams
- Range = 47.7 - 47.5 = 0.2 grams

**Conclusion for Machine 1:**
- The average (47.575 grams) is far from the true value (50.0 grams), indicating that Machine 1 is **less accurate**.
- The measurements are close to each other (range of 0.2 grams), indicating that Machine 1 is **more precise**.

### Step 3: Analyze Measurements from Machine 2
The measurements from Machine 2 are:
- 49.8 grams
- 50.5 grams
- 51.0 grams
- 49.6 grams

**Calculate the average:**
\[ \text{Average} = \frac{(49.8 + 50.5 + 51.0 + 49.6)}{4} = \frac{201.9}{4} = 50.475 \text{ grams} \]

**Determine the range:**
- Minimum = 49.6 grams
- Maximum = 51.0 grams
- Range = 51.0 - 49.6 = 1.4 grams

**Conclusion for Machine 2:**
- The average (50.475 grams) is closer to the true value (50.0 grams) than Machine 1's average, indicating that Machine 2 is **more accurate**.
- The measurements are spread out (range of 1.4 grams), indicating that Machine 2 is **less precise**.

### Step 4: Compare the Results
- **Machine 1:** Less accurate, more precise.
- **Machine 2:** More accurate, less precise.

### Final Answer
Based on the analysis:
- Statement C: "Machine 1 is less accurate and more precise" is correct.
- Statement B: "Machine 2 is more accurate and less precise" is also correct.

Thus, the correct alternatives are **(B) and (C)**.