To find the mean value of the estimates in Fatima's results, we need to follow these steps:
1. Collect All Estimates Together:
Combine all of the data from the table into a single list of values. The table provides the estimates for each of the three persons (A, B, and C) across four trials. We can list out all the values sequentially:
[tex]\[
\begin{align*}
\text{Person A's estimates} & : -3, -1, 0, 2 \\
\text{Person B's estimates} & : 4, -4, 2, -3 \\
\text{Person C's estimates} & : 8, -2, 5, 1 \\
\end{align*}
\][/tex]
When we combine these values into a single list, we get:
[tex]\[
\{-3, 4, 8, -1, -4, -2, 0, 2, 5, 2, -3, 1\}
\][/tex]
2. Sum All Estimates:
Calculate the sum of all the values in the combined list.
[tex]\[
\begin{align*}
-3 + 4 + 8 + (-1) + (-4) + (-2) + 0 + 2 + 5 + 2 + (-3) + 1 &= \\
(4 - 3) + 8 + (-1 - 4) + (-2 + 0 + 2) + 5 + (2 - 3 + 1) &= \\
1 + 8 - 5 + 0 + 5 + 0 &= \\
1 + 8 - 5 + 5 &= \\
14 - 5 &= \\
9
\end{align*}
\][/tex]
3. Count the Number of Estimates:
Count the total number of estimates. Each person has provided 4 estimates, and there are 3 persons, so:
[tex]\[
3 \text{ persons} \times 4 \text{ estimates/person} = 12 \text{ estimates}
\][/tex]
4. Calculate the Mean:
The mean is the total sum of the estimates divided by the number of estimates.
[tex]\[
\text{Mean value} = \frac{\text{Total sum of estimates}}{\text{Number of estimates}} = \frac{9}{12}
\][/tex]
Simplifying the fraction:
[tex]\[
\frac{9}{12} = \frac{3}{4} = 0.75
\][/tex]
So, the mean value in Fatima's results is [tex]\( \boxed{0.75} \)[/tex].
