Fatima conducted an experiment where she asked people to estimate the temperature of glasses of water. She recorded how far the estimates were from the actual temperatures, using positive values for guesses that were too high and negative values for guesses that were too low. Her results are in the table below.

Estimate - actual temperature [tex]\left(^{\circ} C \right)[/tex]

\begin{tabular}{rrr}
Person A & Person B & Person C \\
\hline
-3 & 4 & 8 \\
-1 & -4 & -2 \\
0 & 2 & 5 \\
2 & -3 & 1 \\
\end{tabular}

What is the mean value in Fatima's results?



Answer :

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].