gurmeetgillhhs
Answered

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Which set of data do you believe to be better, your data or your friend's data? Explain your reasoning.

\begin{tabular}{|r|r|r|}
\hline
Sample & Your Mass [tex]$(g)$[/tex] & Friend's Mass [tex]$(g)$[/tex] \\
\hline
1 & 2.4 & 2.55 \\
\hline
2 & 2.6 & 2.51 \\
\hline
3 & 2.4 & 2.62 \\
\hline
4 & 2.2 & 2.48 \\
\hline
5 & 2.6 & 2.44 \\
\hline
6 & 2.4 & 2.55 \\
\hline
7 & 2.6 & 2.51 \\
\hline
8 & 2.4 & 2.52 \\
\hline
9 & 2.2 & 2.46 \\
\hline
10 & 2.4 & 2.49 \\
\hline
\end{tabular}

Sagot :

GinnyAnswer
To determine which set of data is better, we need to analyze both the central tendency (mean) and the dispersion or variability (standard deviation) of the two datasets.

### Your Data

Given the data points:
[tex]\[2.4, 2.6, 2.4, 2.2, 2.6, 2.4, 2.6, 2.4, 2.2, 2.4\][/tex]

1. Mean: The average of your data is
[tex]\[ \text{Your Mean} = 2.42 \][/tex]

2. Standard Deviation: The measure of how spread out your data is
[tex]\[ \text{Your Standard Deviation} = 0.14 \][/tex]

### Friend's Data

Given the data points:
[tex]\[2.55, 2.51, 2.62, 2.48, 2.44, 2.55, 2.51, 2.52, 2.46, 2.49\][/tex]

1. Mean: The average of your friend's data is
[tex]\[ \text{Friend's Mean} = 2.51 \][/tex]

2. Standard Deviation: The measure of how spread out your friend's data is
[tex]\[ \text{Friend's Standard Deviation} = 0.049 \][/tex]

### Comparison

1. Mean:
- Your data has a mean of [tex]\(2.42\)[/tex].
- Your friend's data has a mean of [tex]\(2.51\)[/tex].

2. Standard Deviation:
- Your data has a standard deviation of [tex]\(0.14\)[/tex].
- Your friend's data has a standard deviation of [tex]\(0.049\)[/tex].

### Reasoning

- Mean: The mean indicates the central tendency of the data. Your friend's mean ([tex]\(2.51\)[/tex]) is higher than yours ([tex]\(2.42\)[/tex]), which means that on average, your friend's measured values are closer to your target value if higher is considered better in this context.

- Standard Deviation: The standard deviation indicates how spread out the values are. Your friend's standard deviation ([tex]\(0.049\)[/tex]) is much lower than yours ([tex]\(0.14\)[/tex]). A lower standard deviation suggests that your friend's measurements are more consistent and closer to the mean compared to yours.

### Conclusion

Based on both the mean and the standard deviation, your friend's data appears to be better. The higher mean ([tex]\(2.51\)[/tex]) coupled with a lower standard deviation ([tex]\(0.049\)[/tex]) indicates that your friend's measurements are both more accurate (higher average value) and more precise (less variability) compared to yours.
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