Question

Homework: Section 3.4 Homework Score: 0.5 of 1 pt %) 3.431 The following are amounts of time (minutes) spent on hygiene and grooming in the morning by survey respondents. Determine the 5-number summary and construct a Save Score: 59.85%, 13.17 of 22 pts 14 of 22 (14 complete) ▼ Question Help boxplot for the data given below 4489 11 15 15 15 16 17 20 21 34 36 40 48 54 65 The 5-number summary is (Use ascending order. Type integers or decimals.)

Answer 1

These are the sample data that have been provided with. X (Asc. Order) Position 15 15 15 16 17 20 21 10 12 13 14 15 16 17 18 36 40 65

Based on the table above, the minimum is min 4 and the maximum is max 65. Now the position of the first quartile Q1 is: 25 4.75 L25-100 x (n + 1)-0.25 x 19 interpolating between Since L254.75 is not an integer number, the first quartile Q1 is computed b the values located in the 4th and 5th positions, as shown in the formula below: 01 1(4.75 4) x (15 11 14 Since the sample size n 18 is even, we have that (n +1)/2 (181)/2 9.5 is not an integer value, so the median is computed directly by finding the average of the values located at positions 9th and 10th, which is: 17+20 median 18.5 Now the position of the third quartile Q3 is: 75 100 x (n + 1) L75 0.75 × 19-14.25 Since Ls 14.25 is not an integer number, the third quartile Qs is computed by interpolating between the values located in the 14th and 15th positions, as shown in the formula below Q3 40(14.25 -14) x (48 40) 42

Therefore, based on the results found above, we get the following five-number summary: Minimum 14 18.5 42 65 Median Maximum =

BoxPlot 70 60 40 50 20 340 10 #amount of minutes