Compare the mean of the population with the mean of the sample.
Population Data:
0 3 3 1 3
2 2 2 5 4
3 3 3 0 1
2 0 2 3 3
Sample Data:
5 3 0 2 4
What is the difference between the mean of the sample and the mean of the population?
A. 0.55
B. 1.25
C. 2.25
D. 2.80
Answer (1)
Calculate the population mean: 20 45 = 2.25 .
Calculate the sample mean: 5 14 = 2.8 .
Find the absolute difference between the sample mean and the population mean: ∣2.8 − 2.25∣ = 0.55 .
The difference between the mean of the sample and the mean of the population is 0.55 .
Explanation
Analyze the data First, let's analyze the given data. We have a population dataset and a sample dataset. Our goal is to find the difference between the mean of the sample and the mean of the population.
Calculate the population mean Next, we need to calculate the mean of the population. The population data is: [0, 3, 3, 1, 3, 2, 2, 2, 5, 4, 3, 3, 3, 0, 1, 2, 0, 2, 3, 3]. To find the mean, we sum all the values and divide by the number of values, which is 20.
Calculate the sum and the population mean The sum of the population data is: 0 + 3 + 3 + 1 + 3 + 2 + 2 + 2 + 5 + 4 + 3 + 3 + 3 + 0 + 1 + 2 + 0 + 2 + 3 + 3 = 45 So, the population mean is: 20 45 = 2.25
Calculate the sample mean Now, let's calculate the mean of the sample. The sample data is: [5, 3, 0, 2, 4]. To find the mean, we sum all the values and divide by the number of values, which is 5.
Calculate the sum and the sample mean The sum of the sample data is: 5 + 3 + 0 + 2 + 4 = 14 So, the sample mean is: 5 14 = 2.8
Calculate the difference between the means Now, we need to find the difference between the sample mean and the population mean. The sample mean is 2.8 and the population mean is 2.25. The difference is: ∣2.8 − 2.25∣ = 0.55
Compare and conclude Finally, we compare the calculated difference with the given options. The difference between the mean of the sample and the mean of the population is 0.55.
Examples
Understanding the difference between population and sample means is crucial in various real-world scenarios. For instance, imagine a quality control engineer wants to assess the average weight of products coming off a production line. Instead of measuring every single product (the population), they might take a sample of products to estimate the average weight. By comparing the sample mean to the population mean (if known), they can determine if the sample is representative and if the production process is consistent. This helps in making informed decisions about the quality and consistency of the products.
