Let's analyze the provided box plot to answer the questions about the weight of 600 toys.
The box plot displays five key values: Minimum, First Quartile (Q1), Median (Q2), Third Quartile (Q3), and Maximum.

From the box plot:
- The leftmost whisker ends at the Minimum value.
- The left edge of the box is the First Quartile (Q1).
- The line inside the box is the Median (Q2).
- The right edge of the box is the Third Quartile (Q3).
- The rightmost whisker ends at the Maximum value.

Let's read these values from the scale:
- Minimum: 124 grams
- Q1: 136 grams
- Median (Q2): 142 grams
- Q3: 160 grams
- Maximum: $\(\mathbf{1 8 2}\)$ grams

Now, let's calculate the requested values:
I. The Range

The range is the difference between the maximum and minimum values.
Range $=$ Maximum - Minimum
Range $=182$ grams -124 grams
Range $=58$ grams

II. The Three Quartiles

The three quartiles are Q1, Q2 (Median), and Q3.
- $\mathrm{Q} 1=136$ grams
- Q2 (Median) = 142 grams
- Q3 = 160 grams
III. The Interquartile Range (IQR)

The IQR is the difference between the third quartile (Q3) and the first quartile (Q1).

$$
\(\begin{aligned}
& I Q R=Q 3-Q 1 \\
& I Q R=160 \text { grams }-136 \text { grams } \\
& I Q R=\mathbf{2 4} \text { grams }
\end{aligned}\)
$$

IV. The approximate number of toys that weigh between $\(\mathbf{1 3 6}\)$ and $\(\mathbf{1 4 2}\)$ grams?

In a box plot, the data is divided into four quartiles, with approximately $25 \%$ of the data falling into each quartile.
- The range from the Minimum to Q1 contains approximately $25 %$ of the data.
- The range from Q1 to the Median (Q2) contains approximately $25 %$ of the data.
- The range from the Median (Q2) to Q3 contains approximately $25 %$ of the data.
- The range from Q3 to the Maximum contains approximately $25 %$ of the data.

The question asks for the number of toys that weigh between 136 and 142 grams.
From our readings:
- 136 grams is Q1.
- 142 grams is Q2 (Median).

So, the number of toys weighing between 136 grams (Q1) and 142 grams (Q2) represents approximately the second quartile of the data.
This corresponds to approximately $25 \%$ of the total number of toys.
Total number of toys $=600$.
Approximate number of toys between 136 and 142 grams $=25 \%$ of 600

$$
\(\begin{aligned}
& =0.25 * 600 \\
& =150 \text { toys }
\end{aligned}\)
$$


The approximate number of toys that weigh between 136 and 142 grams is 150.