Question

the data set represents the number of eggs produced by a small group of chickens each day for 10 days. 7 7 7 7 7 8 8 8 8 9. select all the values that could represent the typical number of eggs produced in a day. a 7.5 eggs b 7.6 eggs c 7.7 eggs d 8 eggs e 9 eggs. from unit 1, lesson 2. the dot - plot displays the lengths of pencils (in inches) used by students in a class. what is the mean?

Explanation:

Step1: Calculate the mean of the egg - production data

The data set for egg production is \(7,7,7,7,7,8,8,8,8,9\). The formula for the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(n = 10\), \(\sum_{i=1}^{10}x_{i}=7\times5 + 8\times4+9\times1=35 + 32+9=76\). So the mean \(\bar{x}=\frac{76}{10}=7.6\).
The mode (most frequent value) is \(7\) and \(8\) (both appear 5 and 4 times respectively). A typical value can be the mean or a mode - like value.

Step2: Calculate the mean of the pencil - length data

From the dot - plot, assume the number of data points: for length \(6\) there is \(1\) point, for length \(6.5\) there are \(2\) points, for length \(7\) there are \(4\) points, for length \(7.5\) there are \(2\) points and for length \(8\) there is \(1\) point. \(n=1 + 2+4 + 2+1=10\). \(\sum_{i = 1}^{n}x_{i}=6\times1+6.5\times2 + 7\times4+7.5\times2+8\times1=6+13 + 28+15+8=70\). The mean \(\bar{x}=\frac{70}{10}=7\).

Answer:

For the egg - production problem: B. 7.6 eggs, D. 8 eggs
For the pencil - length problem: 7 inches