Question

select the correct answer.

in an attempt to be environmentally friendly, the city council decides that there must be at least 18 trees on each block in the city. a sample of 20 blocks was randomly surveyed, with these results (number of trees per block):
24, 17, 7, 20, 28, 27, 10, 21, 30, 8, 30, 27, 22, 27, 27, 13, 27, 20, 24, 17
what is the sample mean number of trees per block \\(\bar{x}\\)?

\\(\bigcirc\\) a. \\(\\ 24\\)
\\(\bigcirc\\) b. \\(\\ 17.7\\)
\\(\bigcirc\\) c. \\(\\ \text{there is insufficient data to answer this question.}\\)
\\(\bigcirc\\) d. \\(\\ 21.3\\)

Explanation:

Step1: Sum all the tree counts

First, we add up all the numbers of trees per block:
\(24 + 17 + 7 + 20 + 28 + 27 + 10 + 21 + 30 + 8 + 30 + 27 + 22 + 27 + 27 + 13 + 27 + 20 + 24 + 17\)
Let's calculate step - by - step:
\(24+17 = 41\); \(41 + 7=48\); \(48+20 = 68\); \(68+28 = 96\); \(96+27 = 123\); \(123+10 = 133\); \(133+21 = 154\); \(154+30 = 184\); \(184+8 = 192\); \(192+30 = 222\); \(222+27 = 249\); \(249+22 = 271\); \(271+27 = 298\); \(298+27 = 325\); \(325+13 = 338\); \(338+27 = 365\); \(365+20 = 385\); \(385+24 = 409\); \(409+17 = 426\)

Step2: Calculate the sample mean

The formula for the sample mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(n = 20\) (the number of blocks surveyed) and \(\sum_{i=1}^{n}x_{i}=426\).
So, \(\bar{x}=\frac{426}{20}=21.3\)

Answer:

D. 21.3