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In the 1830s, land surveyors began to study the land acquired in the Louisiana Purchase. Part of their task was to note the sizes of trees they encountered. The table of data below is for bur oak trees measured during the survey. As an example of interpretation, the third row of data shows that there were 19 trees that each had a diameter of six inches. There were a total of 431 bur oak trees recorded.

Tree Diameter (inches) Frequency (count) Cumulative Frequency Percentile
4 2 2 0.005
5 2 7 0.016
6 19 26 0.060
7 5 31 0.072
8 41 72 0.167
9 12 84 0.195
10 53 137 0.318
11 3 140 0.325
12 64 204 0.473
13 4 208 0.483
14 46 254 0.589
15 11 265 0.615
16 48 313 0.726
17 2 315 0.731
18 47 362 0.840
19
20 30 392 0.910
21
22 4 396 0.919
23
24 18 414 0.961
25
26 1 415 0.963
27
28 2 417 0.968
29
30 8 425 0.986
31
32
33
34 1 426 0.988
35 1 427 0.991
36 3 430 0.998
37
38 1 431 1.000

Decide whether the following statements are true or false about this scenario.

True

False

The mode of the tree diameter measurements is 12 inches

The proportion of trees that had a diameter of at least 7 inches but at most 9 inches is 0.123

The 75th percentile of tree diameter measurements is 17 inches.

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