The weights of a sample of crates ready for shipment to Laos are (in kilograms): 103, 97, 101, 106 and 103. What is the mean deviation?
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A. B. C. D. E.A
The mean is 102. The mean deviation is the absolute values of the deviation from the mean. (1 + 5 + 1 + 4 + 1)/5 = 12/5 = 2.4
To calculate the mean deviation, you need to follow these steps:
Step 1: Find the mean (average) of the data set. Step 2: Calculate the absolute deviation for each data point by subtracting the mean from each data point. Step 3: Calculate the mean of the absolute deviations.
Let's calculate the mean deviation for the given sample of crate weights.
Step 1: Find the mean (average) of the data set. The weights of the crates are: 103, 97, 101, 106, and 103. To find the mean, add up all the weights and divide by the number of data points:
Mean = (103 + 97 + 101 + 106 + 103) / 5 = 510 / 5 = 102 kg
So, the mean weight is 102 kg.
Step 2: Calculate the absolute deviation for each data point. To find the absolute deviation, subtract the mean from each data point and take the absolute value. Here are the calculations:
|103 - 102| = 1 kg |97 - 102| = 5 kg |101 - 102| = 1 kg |106 - 102| = 4 kg |103 - 102| = 1 kg
Step 3: Calculate the mean of the absolute deviations. To find the mean deviation, calculate the average of the absolute deviations. Add up all the absolute deviations and divide by the number of data points:
Mean Deviation = (1 + 5 + 1 + 4 + 1) / 5 = 12 / 5 = 2.4 kg
Therefore, the mean deviation of the crate weights is 2.4 kg.
The correct answer is option A: 2.4 kg.