Question

part: 1 / 2
part 2 of 2
analyze the data.
the times range from 11 to 33 minutes. there are gaps at 16 and \boxed{} minutes with a peak at \boxed{} minutes. there are three clusters. the first cluster is from 11 to \boxed{} minutes, the second cluster is from 17 to \boxed{} minutes, and the third cluster is from 28 to \boxed{} minutes.

Explanation:

Step1: Identify the gap after 16

Looking at the number line, after 16, the next gap is at 23 (since there are no dots between 16 and 17? Wait, no, the x - axis is 10,11,12,...35. The first gap: after 16, the next non - empty is 17? Wait, no, let's check the dots. The first cluster: 11 - 15 (dots at 11,12? Wait no, the first set of dots: 11 has dots, 12 has 1, 13 has 1, 14 has 2, 15 has 3? Wait, maybe better to look at the gaps. The first gap: between 15 and 17 (since 16 has no dots). Then the next gap: between 22 and 25? Wait, 23 and 24 have no dots? Wait, the x - axis labels: 10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35.

Looking at the dots:

• 11: dots
• 12: 1 dot
• 13: 1 dot
• 14: 2 dots
• 15: 3 dots
• 16: 0 dots (gap)
• 17: 2 dots
• 18: 2 dots
• 19: 4 dots
• 20: 4 dots
• 21: 5 dots (peak here? Wait 21 has the most dots)
• 22: 2 dots
• 23: 0 dots
• 24: 0 dots
• 25: 3 dots
• 26: 2 dots
• 27: 0 dots? No, 28: 3 dots, 29: 2 dots, 30: 3 dots, 31: 2 dots, 32: 4 dots, 33: 1 dot, 34: 1 dot, 35: 0 dots.

Wait, let's re - examine:

Gap at 16 (no dots), then next gap: 23 and 24? Wait 23 and 24 have no dots? Wait 25 has dots. So gap at 23 (and 24? But the question says "gaps at 16 and [ ] minutes". So probably 23 (since 23 has no dots).

Peak: the number with the most dots. At 21, how many dots? Let's count: 11: 4, 12:1,13:1,14:2,15:3,16:0,17:2,18:2,19:4,20:4,21:5,22:2,23:0,24:0,25:3,26:2,27:0? No, 28:3,29:2,30:3,31:2,32:4,33:1,34:1,35:0. So 21 has 5 dots, which is the peak.

First cluster: 11 - 15 (since 16 is a gap). Second cluster: 17 - 22 (since 23 - 24 are gaps). Third cluster: 28 - 34 (since 27 is a gap? Wait 25 - 27: 25 has 3,26 has 2,27 has 0? No, 28 has 3, so third cluster from 28 to 34 (since 35 has 0).

So:

• Gaps at 16 and 23 minutes.
• Peak at 21 minutes.
• First cluster: 11 to 15 minutes.
• Second cluster: 17 to 22 minutes.
• Third cluster: 28 to 34 minutes.

Step2: Fill in the blanks

• Gaps: 16 and 23.
• Peak: 21.
• First cluster: 11 - 15.
• Second cluster: 17 - 22.
• Third cluster: 28 - 34.

Answer:

Gaps at 16 and $\boldsymbol{23}$ minutes, peak at $\boldsymbol{21}$ minutes. First cluster 11 - $\boldsymbol{15}$, second 17 - $\boldsymbol{22}$, third 28 - $\boldsymbol{34}$.