To find the range of the median number of hours of TV watched, we first need to determine the total number of students surveyed.
1. Calculate Total Enrollment
We sum the number of students in each range (bin) of the histogram:
Attachment:
GRe data.png [ 29.82 KiB | Viewed 54 times ]
The total number of students $(N)$ is 86 .
2. Locate the Median Position
The median is the middle value when the data is ordered. For an even number of data points ( $N=86$ ), the median lies between the $\(\frac{N}{2}\)$th alue and the $\((\frac{N}{2} + 1)\)$th value.
- $\(\frac{86}{2}=43\)$
- $\(\frac{86}{2}+1=44\)$
The median is the average of the $\(\mathbf{4 3}^{\text {rd }}\)$ and $\(\mathbf{4 4}^{\text {th }}\)$ values. Since the median will fall within a specific range (bin), we can determine the range by finding where the $\(43^{\text {rd }}\)$ and $\(44^{\text {th }}\)$ values are located using the cumulative frequency.
3. Determine the Median Range
We find the cumulative count:
- Range 1-5: Students 1 through 13. (Count: 13 )
- Range 6-10: Students 14 through $\(13+35=\mathbf{4 8}\)$.
Since the $\(\mathbf{4 3}^{\text {rd }}\)$ and $\(\mathbf{4 4}^{\text {th }}\)$ students both fall within the $\(\mathbf{6 - 1 0}\)$ hour range, the median number of hours of TV watched must be within this range.
The correct range for the median is B. 6-10.