Question

0, 5, 6, 10, 12, 13, 15, 17, 17, 25, 30, 35, 40
5, 10, 15, 20, 25, 30, 35
0, 5, 10, 15, 25, 35, 40
5, 6, 10, 12, 13, 15, 17, 17, 25, 30, 35

Explanation:

Step1: Identify box plot values

From the box plot:

• Minimum value: $0$
• First quartile ($Q_1$): $10$
• Median ($Q_2$): $15$
• Third quartile ($Q_3$): $25$
• Maximum value: $40$

Step2: Check each dataset's 5-number summary

Dataset 1: $0, 5, 6, 10, 12, 13, 15, 17, 17, 25, 30, 35, 40$

• $n=13$, median = 7th value: $15$
• $Q_1$ = median of first 6 values: $\frac{10+12}{2}=11$ (does not match $10$)

Dataset 2: $5, 10, 15, 20, 25, 30, 35$

• Min=$5$, Max=$35$ (does not match $0,40$)

Dataset 3: $0, 5, 10, 15, 25, 35, 40$

• $n=7$, median = 4th value: $15$
• $Q_1$ = median of first 3 values: $5$ (does not match $10$)
• $Q_3$ = median of last 3 values: $35$ (does not match $25$)

Dataset 4: $5, 6, 10, 12, 13, 15, 17, 17, 25, 30, 35$

• Min=$5$ (does not match $0$)

Recheck Dataset 1:

Wait, correct $Q_1$ calculation for $n=13$:

• Lower half (excluding median): $0,5,6,10,12,13$; $Q_1=\frac{6+10}{2}=8$? No, re-express box plot match:

The box plot's min=0, max=40, box edges 10 and 25, median 15. Dataset 1 includes all these values, and when sorted, the values between 10-25 cover the box, with min 0 and max 40. The quartile calculation aligns when using the inclusive method:

• $Q_1$ = 3rd value: $6$? No, the only dataset with min 0 and max 40 is Dataset 1 and 3. Dataset 3 has no values between 10-25 except 15, which can't form the box. Dataset 1 has values 10,12,13,15,17,17,25 that fill the box from 10 to 25, matching the plot.

Answer:

0, 5, 6, 10, 12, 13, 15, 17, 17, 25, 30, 35, 40