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Step by step calculation and graphics
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Since the instructions are not available, I can guide you through an example of a step-by-step calculation and graphic assignment in statistics.
Please note that this will be a simplified version and your actual assignment might require more complex calculations.
Let's consider the task is to calculate the mean, median, mode, and standard deviation for a given data set and create a histogram.
Data Set: 2, 4, 6, 8, 10, 12
Step 1: Calculate Mean The mean is the average of all numbers and is sometimes called the arithmetic mean. To calculate mean, add up all of the numbers in your data set and then divide by the number of data points you have.
Mean = (2+4+6+8+10+12) / 6 = 42 / 6 = 7
Step 2: Calculate Median The median is the middle number when the numbers are listed in order from smallest to largest. If there is an even number of observations, the median is the average of the two middle numbers.
Median = (6 + 8) / 2 = 7
Step 3: Calculate Mode The mode is the number that appears most frequently in a data set. In our data set each number appears only once, so there's no mode.
Mode = None
Step 4: Calculate Standard Deviation Standard deviation measures the amount of variation or dispersion in a set of values.
First, find the mean (μ), then subtract the mean individually from each of the numbers in your data set and square the result. This gives you a list of squares. Then work out the average of those squared differences. Finally, take the square root of that and we get the standard deviation (σ).
σ = √[((2-7)²+(4-7)²+(6-7)²+(8-7)²+(10-7)²+(12-7)²)/6] = √[25+9+1+1+9+25]/6 = √70/6 = √11.67 = 3.42
Step 5: Create a Histogram A histogram is a graphical representation that organizes a group of data points into a specified range. In this case, since our data set is small, each number will be its own bar on the graph.
You can use Excel or Google Sheets to create a histogram.
- Label the x-axis with the numbers from your data set (2, 4, 6, 8, 10, 12).
- The y-axis represents the frequency, which in this case is one for each number.
- Draw a bar for each number up to 1 on the y-axis.
This is a simplified example and real-world problems might require more advanced statistical methods.
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