Problem 5 - Basic Statistics for Business and Economics with Student

Question

Compute the mean of the following sample values: 16.25,12.91,14.58

Step-by-Step Solution

Answer

The mean of the sample values is 14.58.

Step 1: Sum the Sample Values

Add up all the given sample values together. The values are 16.25, 12.91, and 14.58. \[16.25 + 12.91 + 14.58 = 43.74\]

Step 2: Count the Number of Sample Values

Determine how many values are in the sample. The sample consists of the values: 16.25, 12.91, and 14.58, so there are 3 values in total.

Step 3: Divide the Sum by the Number of Values

Divide the total sum obtained in Step 1 by the number of values from Step 2 to find the mean.\[\text{Mean} = \frac{43.74}{3} = 14.58\]

Key Concepts

Mean

The concept of the mean is a cornerstone of statistics and data analysis. In simple terms, the mean is the average value of a set of numbers. It's like finding the middle ground—the number that best represents all the numbers in a dataset. To compute the mean, you follow a straightforward process. Sum up all the numbers in your dataset and then divide this sum by the total number of numbers you've added.
For example, if you have the numbers 4, 8, and 12, you first add them: 4 + 8 + 12, which equals 24. Then divide by 3 (the total number of numbers): \[ \text{Mean} = \frac{24}{3} = 8 \] This gives us a mean of 8. This process is a great way to summarize data to get an overall sense of the whole dataset.

Sample Values

Sample values are individual data points collected in a study or experiment. In statistical terms, they come from a larger group called the population. The sample is just a snapshot or a small piece of this bigger picture.
When we work with sample values, we’re often trying to learn or say something about the entire population, without having to collect data from everyone. This makes it much more practical and manageable.
To compute the mean from sample values, start by listing all the values. Each number in this list contributes to calculating the mean, as seen in the given example with sample values 16.25, 12.91, and 14.58.

Step by Step Solution

Understanding the mean calculation becomes much easier when you break it down into simple steps. Let's explore the step-by-step method to make it crystal clear:

• Step 1: Sum the Sample Values - Begin by adding all your data points together to find their sum. For instance, with the values 16.25, 12.91, and 14.58, the sum equals 43.74, because \[ 16.25 + 12.91 + 14.58 = 43.74 \].
• Step 2: Count the Number of Sample Values - Determine how many values you have in total. Here, it’s simply counting each data point, which totals 3 values.
• Step 3: Calculate the Mean - Lastly, divide the sum from Step 1 by the count from Step 2. Apply it as: \[ \text{Mean} = \frac{43.74}{3} = 14.58 \]. This gives you the average or mean value of your sample.

These steps provide a clear path to easily compute the mean of any dataset. Remember, practice makes perfect, so try these steps with different samples to build your confidence.