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Question
a blowhole is a hole in a cliff that produces eruptions of water when the ocean swell hits the cliff. below are 40 times (in seconds) between eruptions for the kiama blowhole in australia. time between eruptions histogram and stem - and - leaf plot shown based on the graphs, are there any apparent outliers in this distribution? there are no apparent outliers. there are three apparent outliers. there is one apparent outlier. there are two apparent outliers.
Looking at the stem - and - leaf plot and the histogram, we observe that most of the data points are concentrated at lower values (smaller time intervals between eruptions). In the stem - and - leaf plot, the stem 16 has a leaf 9 (representing 169 seconds) and the stem 15 has no leaves, stem 14 has no leaves, etc. In the histogram, there is a very small bar at the higher end (around 150 - 200 range) and one data point at 169. Also, looking at the spread, the data point at 169 (and maybe 91? Wait, no, the stem - and - leaf: stem 16 (169), stem 9 (91), but 91 is closer to the main cluster? Wait, no, the main cluster is at lower stems (0 - 8 mostly). Wait, the stem 16 has count 1 (169), and stem 9 has count 1 (91), but 91 is in the 90s, while the main cluster is below 100? Wait, no, the histogram has bins: 0 - 50, 50 - 100, 100 - 150, 150 - 200. The bar at 150 - 200 is very small, and the stem - and - leaf has 16|9 (169) and maybe 9|1 (91). Wait, no, 91 is in the 90s, which is in the 50 - 100 bin? Wait, no, 0 - 50, 50 - 100, 100 - 150, 150 - 200. So 91 is in 50 - 100? Wait, no, 91 is 91, so 50 - 100. But 169 is in 150 - 200. Wait, the stem - and - leaf: let's count the counts. Stem 0:5, stem1:13, stem2:6, stem3:2, stem4:2, stem5:2, stem6:5, stem7:1, stem8:2, stem9:1, stem16:1. So the data points at stem 9 (91) and stem 16 (169)? Wait, no, 91 is 91, which is not that far from the main cluster? Wait, the main cluster is at stem 0 (0 - 9), stem1 (10 - 19), stem2 (20 - 29), etc. Wait, the stem 16 (169) is a very high value compared to the rest. Also, is there another? Wait, the stem 9 has 91, but 91 is in the 90s, and the main cluster is below 100? Wait, no, the stem 6 is 60 - 69, stem7 is 70 - 79, stem8 is 80 - 89, stem9 is 90 - 99. So 91 is in 90 - 99, which is adjacent to 80 - 89 (stem8). But 169 is in 160 - 169, which is way above the rest. Wait, but the stem - and - leaf also has stem 15,14,13,12,11,10 with count 0, except stem16 with count 1. So the data point at 169 (16|9) is an outlier, and is there another? Wait, the stem 9 has 91 (9|1), but 91 is not that far. Wait, maybe I misread. Wait, the histogram: the first bar (0 - 50) is tall, then 50 - 100, then 100 - 150, then a very small bar at 150 - 200. The stem - and - leaf: stem 16 has 1 data point (169), stem 9 has 1 (91), stem 8 has 2 (82,89), stem7 has 1 (77), stem6 has 5, etc. Wait, but 169 is much higher than the rest. Also, is 91 an outlier? No, because 91 is in the 90s, and the data has points up to 89 (stem8:82,89), so 91 is close. But 169 is way above. Wait, but the option says "two apparent outliers"? Wait, no, wait the stem - and - leaf: stem 16 (169) and stem 9 (91)? No, maybe I made a mistake. Wait, let's check the counts. The total number of data points: 5 (stem0)+13 (stem1)+6 (stem2)+2 (stem3)+2 (stem4)+2 (stem5)+5 (stem6)+1 (stem7)+2 (stem8)+1 (stem9)+1 (stem16) = 5 + 13=18, +6=24, +2=26, +2=28, +2=30, +5=35, +1=36, +2=38, +1=39, +1=40. So there are two data points that are far from the main cluster: 91 (9|1) and 169 (16|9)? Wait, no, 91 is 91, and the main cluster is below 100? Wait, no, the main cluster is at lower stems (0 - 8), and 91 is in 90 - 99, which is a bit above, but 169 is way above. Wait, but the option "There are two apparent outliers" – maybe 91 and 169? Wait, but let's look at the histogram. The histogram has a bar at 0 - 50 (tall), 50 - 100 (shorter), 100 - 150 (shorter), and a very small bar at 150 - 200. The data point at 169 is in 150 - 200, and the data point at 91 is in 50 - 100? No, 91 is in 90 - 99, which is part of 50 - 100? Wait, 50 - 100…
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There are two apparent outliers.