Question

1. use tools eight chickens on a farm are weighed. their weights are 5.8, 6.1, 5.5, 6.0, 7.1, 5.9, 6.2, and 5.7 pounds. what are the mean and the mean absolute deviation of the weights? state what strategy and tool you will use to answer the question, explain your choice, and then find the answer.

1. look at the histogram. which statement best describes the data shown in the graph?

a the data have a peak at 13 to 16.
b the data have an outlier at 0 and 10.
c the data have a cluster from 13 to 20.
d the data are approximately symmetric.
histogram: title \weekly hours of practice\, x - axis \practice time (hours)\, y - axis \violin students\, bars with some heights, and violin students icons below.

Explanation:

Question 8

Step 1: Find the mean

First, sum all the weights: \(5.8 + 6.1 + 5.5 + 6.0 + 7.1 + 5.9 + 6.2 + 5.7\). Let's calculate that: \(5.8+6.1 = 11.9\); \(11.9+5.5 = 17.4\); \(17.4+6.0 = 23.4\); \(23.4+7.1 = 30.5\); \(30.5+5.9 = 36.4\); \(36.4+6.2 = 42.6\); \(42.6+5.7 = 48.3\). Then divide by the number of data points (8): \(\text{Mean} = \frac{48.3}{8} = 6.0375\) pounds.

Step 2: Find the mean absolute deviation (MAD)

First, find the absolute difference between each data point and the mean:

• \(|5.8 - 6.0375| = 0.2375\)
• \(|6.1 - 6.0375| = 0.0625\)
• \(|5.5 - 6.0375| = 0.5375\)
• \(|6.0 - 6.0375| = 0.0375\)
• \(|7.1 - 6.0375| = 1.0625\)
• \(|5.9 - 6.0375| = 0.1375\)
• \(|6.2 - 6.0375| = 0.1625\)
• \(|5.7 - 6.0375| = 0.3375\)

Now sum these absolute differences: \(0.2375 + 0.0625 + 0.5375 + 0.0375 + 1.0625 + 0.1375 + 0.1625 + 0.3375\). Let's calculate: \(0.2375+0.0625 = 0.3\); \(0.3+0.5375 = 0.8375\); \(0.8375+0.0375 = 0.875\); \(0.875+1.0625 = 1.9375\); \(1.9375+0.1375 = 2.075\); \(2.075+0.1625 = 2.2375\); \(2.2375+0.3375 = 2.575\). Then divide by the number of data points (8): \(\text{MAD} = \frac{2.575}{8} = 0.321875\) pounds.

• Option A: The peak (highest bar) in the histogram is around 13 - 16, so this is correct.
• Option B: Outliers are extreme values, but 0 and 10 don't seem to be outliers here (the bars at 0 and 10 are small but not extreme compared to the rest).
• Option C: A cluster is a group of data points, but 13 - 20 is where the peak is, but the description of "cluster" isn't as accurate as the peak description.
• Option D: The data isn't symmetric; it has a peak on one side.

Answer:

Mean: \(6.0375\) pounds, Mean Absolute Deviation: \(0.321875\) pounds

Question 9