Question

a 64 - acre coconut farm is arranged in an 8 - by - 8 array. mika wants to know the average number of coconut palms on each acre. each cell in the table represents an acre of land. the number in each cell tells how many coconut palms grow on that particular acre.
the numbers in green represent mikas random sample of 10 acres. what is the average number of coconut palms on the randomly selected acres? round your answer to the nearest tenth.
the average number of coconut palms is \boxed{}.

Explanation:

Step1: Identify the green cells (sample data)

The green - colored cells (Mika's random sample of 10 acres) have the following values: 51, 56, 57, 43, 60, 34, 39, 37, 42, 58.

Step2: Calculate the sum of the sample data

We sum up these 10 numbers:
\[

$$\begin{align*} &51 + 56+57 + 43+60+34+39+37+42+58\\ =&(51 + 56)+(57 + 43)+(60)+(34 + 39)+(37 + 42)+58\\ =&107+100 + 60+(73)+(79)+58\\ =&107+100+60 + 73+79+58\\ =&207+60+73 + 79+58\\ =&267+73+79 + 58\\ =&340+79+58\\ =&419+58\\ =&477 \end{align*}$$

\]

Step3: Calculate the average

The formula for the average (mean) of a sample is \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(n = 10\) and \(\sum_{i=1}^{n}x_{i}=477\).
So, \(\bar{x}=\frac{477}{10}=47.7\)

Answer:

\(47.7\)