To determine the mean (arithmetic average) weight of students based on the provided data, we follow these steps:
### Step 1: Understand the Data
We have the measured weights of students along with the number of students corresponding to each weight.
### Step 2: Organize the Data
We need to extract all the unique weights and their corresponding number of students:
[tex]\[
\begin{aligned}
&\text{Weights: } & [105, 110, 112, 113, 115, 116, 117, 118, 120, 121, 125, 126, 128, 130, 132, 134, 135, 140, 141, 150] & \\
&\text{Number of Students: } & [1, 2, 2, 3, 2, 5, 4, 7, 5, 5, 4, 5, 2, 1, 3, 1, 3, 2, 2, 1] &
\end{aligned}
\][/tex]
### Step 3: Calculate the Total Number of Students
Sum the number of students corresponding to each weight:
[tex]\[
\text{Total number of students} = 1 + 2 + 2 + 3 + 2 + 5 + 4 + 7 + 5 + 5 + 4 + 5 + 2 + 1 + 3 + 1 + 3 + 2 + 2 + 1 = 60
\][/tex]
### Step 4: Calculate the Weighted Sum of the Weights
Each weight needs to be multiplied by the number of students with that weight:
[tex]\[
\begin{aligned}
\text{Weighted sum} &= 105 \times 1 + 110 \times 2 + 112 \times 2 + 113 \times 3 + 115 \times 2 \\
&\quad + 116 \times 5 + 117 \times 4 + 118 \times 7 + 120 \times 5 + 121 \times 5 \\
&\quad + 125 \times 4 + 126 \times 5 + 128 \times 2 + 130 \times 1 + 132 \times 3 \\
&\quad + 134 \times 1 + 135 \times 3 + 140 \times 2 + 141 \times 2 + 150 \times 1 \\
&= 105 + 220 + 224 + 339 + 230 + 580 + 468 + 826 + 600 + 605 + 500 + 630 + 256 + 130 + 396 + 134 + 405 + 280 + 282 + 150 \\
&= 7360
\end{aligned}
\][/tex]
### Step 5: Calculate the Mean Weight
Divide the weighted sum of the weights by the total number of students to find the mean weight:
[tex]\[
\text{Mean weight} = \frac{\text{Weighted sum}}{\text{Total number of students}} = \frac{7360}{60} \approx 122.67
\][/tex]
### Final Answer:
The arithmetic mean (average) weight of the students is approximately [tex]\( 122.67 \)[/tex] pounds.
