To find the interval where the median test score falls, we need to analyze the histogram provided in the image. The steps are as follows:

1. Total Number of Students: We sum up the frequencies of all intervals.
2. Determine Median Position: The median is the middle value in a data set. So, if there are $n$ students, the median will be at the $\frac{n + 1}{2}$th position if $n$ is odd, or the average of the $\frac{n}{2}$th and $\frac{n}{2} + 1$th positions if $n$ is even.
3. Locate the Interval Containing the Median: By adding up the frequencies cumulatively, we can find in which interval this median position falls.

Let's analyze the data from the histogram.

1. Frequency Data from Histogram:

   • $40-49$ points: 2 students
   • $50-59$ points: 8 students
   • $60-69$ points: 14 students
   • $70-79$ points: 9 students
   • $80-89$ points: 7 students
   • $90-99$ points: 2 students

2. Total Number of Students: $2 + 8 + 14 + 9 + 7 + 2 = 42 \text{ students}$

3. Median Position: $\text{Median is the average of the } \frac{42}{2} = 21\text{st and the } 22\text{nd values}.$

4. Cumulative Frequency:

   • Up to $40-49$: $2$ students
   • Up to $50-59$: $2 + 8 = 10$ students
   • Up to $60-69$: $10 + 14 = 24$ students
   • Up to $70-79$: $24 + 9 = 33$ students
   • Up to $80-89$: $33 + 7 = 40$ students
   • Up to $90-99$: $40 + 2 = 42$ students

5. Conclusion: The 21st and 22nd students are within the cumulative frequency range for the $60-69$ interval. Thus, the median test score falls within the $60-69$ points interval.

Would you like any more details or have any further questions?

Related Questions

1. What would the median be if one of the frequencies changed?
2. How would you determine the mode of the distribution?
3. Can you find the range of the quiz scores?
4. How do you calculate the mean from this histogram?
5. What is the impact of outliers on the median in this dataset?

Tip: When interpreting histograms, always check the intervals and cumulative frequencies to locate medians and other central tendencies.