Question

which box plot represents the data in this frequency table? value 0 2 3 4 5 frequency 1 4 5 7 3 figure a figure b figure c figure d incorrect. you have probably miscalculated the value of the quartiles. try again.

Explanation:

Step1: Find total number of data - points

The total number of data - points is the sum of the frequencies. So, $1 + 4+5 + 7+3=20$.

Step2: Arrange the data set

The data set is: $0,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5$.

Step3: Find the median (Q2)

Since $n = 20$ (an even - numbered data set), the median is the average of the 10th and 11th ordered data values. The 10th value is 3 and the 11th value is 4, so $Q2=\frac{3 + 4}{2}=3.5$.

Step4: Find the lower half and Q1

The lower half of the data set consists of the first 10 values: $0,2,2,2,2,3,3,3,3,3$. Since $n = 10$ (even), $Q1$ is the average of the 5th and 6th ordered values. The 5th value is 2 and the 6th value is 3, so $Q1=\frac{2 + 3}{2}=2.5$.

Step5: Find the upper half and Q3

The upper half of the data set consists of the last 10 values: $4,4,4,4,4,4,4,5,5,5$. Since $n = 10$ (even), $Q3$ is the average of the 5th and 6th ordered values. The 5th value is 4 and the 6th value is 4, so $Q3 = 4$.

Step6: Identify the minimum and maximum

The minimum value is 0 and the maximum value is 5.

The box - plot that has a minimum of 0, $Q1 = 2.5$, median of 3.5, $Q3 = 4$, and maximum of 5 is figure B.

Answer:

figure B