Question

question #2
the data in the box represents the daily high temperature (°f) in a city for 2 weeks.
62, 61, 58, 58, 60, 55, 61, 54, 55, 58, 62, 61, 57, 59
which box plot represents this data?

Explanation:

Step1: Arrange data in ascending order

52, 54, 55, 55, 56, 56, 57, 58, 59, 61, 61, 62, 62, 62

Step2: Find the minimum value

The minimum value is 52.

Step3: Find the first - quartile (Q1)

There are 14 data points. The position of Q1 is $\frac{14 + 1}{4}=3.75$. So, Q1 is between the 3rd and 4th ordered data points, $Q1=\frac{55 + 55}{2}=55$.

Step4: Find the median (Q2)

The position of the median is $\frac{14+1}{2}=7.5$. So, $Q2=\frac{57 + 58}{2}=57.5$.

Step5: Find the third - quartile (Q3)

The position of Q3 is $3\times\frac{14 + 1}{4}=11.25$. So, Q3 is between the 11th and 12th ordered data points, $Q3=\frac{61+62}{2}=61.5$.

Step6: Find the maximum value

The maximum value is 62.

Step7: Match with box - plots

We look for a box - plot with minimum 52, Q1 = 55, median = 57.5, Q3 = 61.5, and maximum 62.

Answer:

The box - plot that represents the data needs to have the minimum value at 52, the first - quartile at 55, the median at 57.5, the third - quartile at 61.5, and the maximum value at 62. Without seeing the exact details of the box - plots in a clear way, but based on the calculated values, we would match these values to the appropriate box - plot among A, B, C, D. If we assume the box - plots are drawn correctly in terms of the quartile and extreme values representation, we would choose the one that aligns with our calculated values. If we had to guess without seeing the plots precisely, we note the key values: min = 52, Q1 = 55, med = 57.5, Q3 = 61.5, max = 62 and look for the corresponding box - plot.