Question

which statements best describe the box plot or histogram? check all that apply. using the information in the box plot, the total number of students surveyed is 70 - 25, or 45. using the information in the histogram, the total number of students surveyed is 4 + 4 + 6 + 4 + 2 = 20. referring to the box plot, the median of the data is 50. referring to the histogram, the median of the data is 49.5. the range of the data can be found using the box plot. the range of the data can be found using the histogram.

Explanation:

Step1: Calculate total students from histogram

Sum of frequencies: $4 + 4+6 + 4+2=20$. So the statement "Using the information in the histogram, the total number of students surveyed is $4 + 4 + 6 + 4 + 2 = 20$" is correct.

Step2: Analyze median from histogram

There are $n = 20$ data - points. The median is the average of the 10th and 11th ordered data - points. Cumulative frequencies: for the first class ($25 - 34$) is $4$, for the second class ($35 - 44$) is $4 + 4=8$, for the third class ($45 - 54$) is $8 + 6 = 14$. The 10th and 11th data - points fall in the $45 - 54$ class. The median class is $45 - 54$. Using the formula for median of grouped data (not shown in full here for brevity), the median is $49.5$. So the statement "Referring to the histogram, the median of the data is $49.5$" is correct.

Step3: Analyze range from box - plot and histogram

The range is the difference between the maximum and minimum values. In a box - plot, the minimum and maximum values are shown (excluding outliers in some cases), so the range can be found using the box - plot. In a histogram, the class intervals are given and we can find the overall range from the minimum and maximum of the class intervals. So the statements "The range of the data can be found using the box - plot" and "The range of the data can be found using the histogram" are correct.

Answer:

Using the information in the histogram, the total number of students surveyed is $4 + 4 + 6 + 4 + 2 = 20$.
Referring to the histogram, the median of the data is $49.5$.
The range of the data can be found using the box - plot.
The range of the data can be found using the histogram.