Question

answer the statistical measures and create a box and whiskers plot for the following set of data. enter all values as whole numbers or decimals. 6,7,8,9,9,10,10,10,11,11,12,13,14,15,15 min: □ q1: □ med: □ q3: □ max: □ create the box plot by dragging the lines: box plot image with x - axis from 0 to 20, labeled 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20

Explanation:

Step1: Find Minimum (Min)

The minimum value in the data set is the smallest number. Looking at the data: 6,7,8,9,9,10,10,10,11,11,12,13,14,15,15. The smallest is 6.
Min = 6

Step2: Find Maximum (Max)

The maximum value is the largest number. In the data set, the largest is 15.
Max = 15

Step3: Find Median (Med)

The data set has 15 values (n = 15). The median is the middle value when the data is ordered. For n odd, the median is at position $\frac{n + 1}{2}=\frac{15+1}{2}=8$th term. The ordered data: 6,7,8,9,9,10,10,10,11,11,12,13,14,15,15. The 8th term is 10.
Med = 10

Step4: Find Q1 (First Quartile)

Q1 is the median of the lower half of the data. The lower half is the first 7 values (since n = 15, lower half is before the median): 6,7,8,9,9,10,10. The median of these 7 values (n = 7, position $\frac{7 + 1}{2}=4$th term). The 4th term is 9.
Q1 = 9

Step5: Find Q3 (Third Quartile)

Q3 is the median of the upper half of the data. The upper half is the last 7 values (after the median): 11,11,12,13,14,15,15. The median of these 7 values (n = 7, position $\frac{7 + 1}{2}=4$th term). The 4th term is 13.
Q3 = 13

Answer:

Min: 6, Q1: 9, Med: 10, Q3: 13, Max: 15

For the box - and - whiskers plot:

• The left whisker starts at Min = 6 and ends at Q1 = 9.
• The box starts at Q1 = 9, has the median (Med = 10) inside it, and ends at Q3 = 13.
• The right whisker starts at Q3 = 13 and ends at Max = 15.