Question
Worked examples of histogram
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GPT 3.5
Example 1:
Suppose we have data on the ages of 50 individuals. The ages range from 20 to 60 years and we want to create a histogram to display the distribution of ages.
Age (years): 25, 28, 30, 35, 40, 45, 50, 52, 55, 58, 60
To create a histogram, we first need to determine the number of bins to use. A common rule of thumb is to use the square root of the total number of data points. In this case, we have 50 data points so we will use approximately 7 bins.
Next, we determine the bin width by calculating the range of the data and dividing it by the number of bins:
Range = 60 - 20 = 40
Bin width = Range / Number of bins = 40 / 7 ≈ 5.71
Now, we can create the histogram by dividing the data into the specified number of bins and counting the frequency of data points in each bin:
Bin 1: 20-25 (1)
Bin 2: 26-31 (3)
Bin 3: 32-37 (2)
Bin 4: 38-43 (1)
Bin 5: 44-49 (2)
Bin 6: 50-55 (2)
Bin 7: 56-60 (2)
Finally, we plot the histogram where the x-axis represents the age ranges and the y-axis represents the frequency of data points in each bin.
Example 2:
Suppose we have data on the test scores of 60 students. The test scores range from 60 to 100 and we want to create a histogram to display the distribution of test scores.
Test Scores: 65, 70, 75, 80, 85, 90, 95, 100
Following the same steps as in Example 1, we determine the number of bins, calculate the bin width, divide the data into bins, and count the frequency of data points in each bin.
Since we have 60 data points, we will use approximately 8 bins.
Bin width = Range / Number of bins = 40 / 8 = 5
Bin 1: 60-65 (1)
Bin 2: 66-71 (2)
Bin 3: 72-77 (2)
Bin 4: 78-83 (2)
Bin 5: 84-89 (2)
Bin 6: 90-95 (2)
Bin 7: 96-100 (1)
Finally, we plot the histogram where the x-axis represents the test score ranges and the y-axis represents the frequency of data points in each bin.
Suppose we have data on the ages of 50 individuals. The ages range from 20 to 60 years and we want to create a histogram to display the distribution of ages.
Age (years): 25, 28, 30, 35, 40, 45, 50, 52, 55, 58, 60
To create a histogram, we first need to determine the number of bins to use. A common rule of thumb is to use the square root of the total number of data points. In this case, we have 50 data points so we will use approximately 7 bins.
Next, we determine the bin width by calculating the range of the data and dividing it by the number of bins:
Range = 60 - 20 = 40
Bin width = Range / Number of bins = 40 / 7 ≈ 5.71
Now, we can create the histogram by dividing the data into the specified number of bins and counting the frequency of data points in each bin:
Bin 1: 20-25 (1)
Bin 2: 26-31 (3)
Bin 3: 32-37 (2)
Bin 4: 38-43 (1)
Bin 5: 44-49 (2)
Bin 6: 50-55 (2)
Bin 7: 56-60 (2)
Finally, we plot the histogram where the x-axis represents the age ranges and the y-axis represents the frequency of data points in each bin.
Example 2:
Suppose we have data on the test scores of 60 students. The test scores range from 60 to 100 and we want to create a histogram to display the distribution of test scores.
Test Scores: 65, 70, 75, 80, 85, 90, 95, 100
Following the same steps as in Example 1, we determine the number of bins, calculate the bin width, divide the data into bins, and count the frequency of data points in each bin.
Since we have 60 data points, we will use approximately 8 bins.
Bin width = Range / Number of bins = 40 / 8 = 5
Bin 1: 60-65 (1)
Bin 2: 66-71 (2)
Bin 3: 72-77 (2)
Bin 4: 78-83 (2)
Bin 5: 84-89 (2)
Bin 6: 90-95 (2)
Bin 7: 96-100 (1)
Finally, we plot the histogram where the x-axis represents the test score ranges and the y-axis represents the frequency of data points in each bin.