To determine which class interval contains the median, follow these steps:
1. Calculate the total number of plants:
Sum the frequencies given for each interval:
[tex]\[
1 + 9 + 7 + 13 = 30
\][/tex]
So, there are 30 plants in total.
2. Determine the median position:
Since the total number of plants is 30, the median position is:
[tex]\[
\frac{30 + 1}{2} = 15.5
\][/tex]
This tells us that the median is the average of the 15th and 16th values when the plants are arranged in ascending order.
3. Calculate the cumulative frequency:
Create a cumulative frequency distribution:
[tex]\[
\begin{array}{|c|c|c|}
\hline \text{Height Interval} & \text{Frequency} & \text{Cumulative Frequency} \\
\hline 0 \leqslant h < 10 & 1 & 1 \\
\hline 10 \leqslant h < 20 & 9 & 1 + 9 = 10 \\
\hline 20 \leqslant h < 30 & 7 & 10 + 7 = 17 \\
\hline 30 \leqslant h < 40 & 13 & 17 + 13 = 30 \\
\hline
\end{array}
\][/tex]
4. Identify the median class interval:
We need the interval where the 15th and 16th plants are located:
- For the first interval [tex]\(0 \leqslant h < 10\)[/tex], the cumulative frequency is 1 (insufficient).
- For the second interval [tex]\(10 \leqslant h < 20\)[/tex], the cumulative frequency is 10 (still insufficient).
- For the third interval [tex]\(20 \leqslant h < 30\)[/tex], the cumulative frequency is 17. This means the 15th and 16th plants are in this interval since 10 < 15.5 ≤ 17.
Thus, the class interval containing the median is [tex]\(20 \leqslant h < 30\)[/tex].
So, the answer is:
C
