Mean, Median, Variance, Standard Deviation: Write Your Numbe

Mean Median Variance Standard Deviationwrite Your Number Collection

Write your number collection: any 9-12 positive numbers, that represent a sample data, like number of items sold per day or number of patients in medical office per day and so on. 1) Find the mean, median, and range for your data collection. 2) Calculate standard deviation for your sample (show steps of calculation).

Paper For Above instruction

In this paper, I will demonstrate how to analyze a sample data set by calculating the mean, median, range, and standard deviation. For this purpose, I have selected a sample data set representing the number of patients visiting a medical office per day over a two-week period. The chosen data set consists of 12 values: 15, 18, 22, 20, 17, 19, 21, 23, 16, 20, 18, 19.

Step 1: Calculating the Mean

The mean, or average, is calculated by summing all data points and dividing by the number of points. The sum of these values is:

15 + 18 + 22 + 20 + 17 + 19 + 21 + 23 + 16 + 20 + 18 + 19 = 209

Number of data points = 12

Therefore, the mean is:

Mean = 209 / 12 ≈ 17.42

Step 2: Finding the Median

The median is the middle value when the data is ordered from smallest to largest. First, we arrange the data:

  • 15, 16, 17, 18, 18, 19, 19, 20, 20, 21, 22, 23

Since there are 12 numbers, the median will be the average of the 6th and 7th values:

6th value = 19

7th value = 19

Median = (19 + 19) / 2 = 19

Step 3: Calculating the Range

The range is the difference between the maximum and minimum values in the data set:

Maximum = 23

Minimum = 15

Range = 23 - 15 = 8

Step 4: Calculating the Standard Deviation

The standard deviation measures the dispersion of data points around the mean. For a sample, the formula is:

Standard deviation (s) = √(Σ(xi - x̄)² / (n - 1))

Where x̄ is the mean, n is the number of data points, and Σ indicates the sum over all data points.

First, compute each deviation from the mean and square it:

xixi - x̄(xi - x̄)²
1515 - 17.42 ≈ -2.42(-2.42)² ≈ 5.86
1818 - 17.42 ≈ 0.58(0.58)² ≈ 0.34
2222 - 17.42 ≈ 4.58(4.58)² ≈ 20.98
2020 - 17.42 ≈ 2.58(2.58)² ≈ 6.66
1717 - 17.42 ≈ -0.42(-0.42)² ≈ 0.18
1919 - 17.42 ≈ 1.58(1.58)² ≈ 2.50
2121 - 17.42 ≈ 3.58(3.58)² ≈ 12.81
2323 - 17.42 ≈ 5.58(5.58)² ≈ 31.14
1616 - 17.42 ≈ -1.42(-1.42)² ≈ 2.02
2020 - 17.42 ≈ 2.58(2.58)² ≈ 6.66
1818 - 17.42 ≈ 0.58(0.58)² ≈ 0.34

Next, sum all squared deviations:

Sum = 5.86 + 0.34 + 20.98 + 6.66 + 0.18 + 2.50 + 12.81 + 31.14 + 2.02 + 6.66 + 0.34 ≈ 92.63

Divide by (n - 1) = 11:

Variance ≈ 92.63 / 11 ≈ 8.42

The standard deviation is the square root of variance:

Standard deviation ≈ √8.42 ≈ 2.90

Conclusion

The analysis of the sample data reveals a mean of approximately 17.42, indicating the average number of patients visiting the medical office per day over the period. The median value of 19 suggests that half of the days had 19 or fewer patients. The range of 8 indicates the extent of fluctuation in daily patient numbers. The standard deviation of approximately 2.90 implies moderate variability around the mean, reflecting typical fluctuations in daily patient counts.

Implications

Understanding these descriptive statistics can assist healthcare administrators in resource planning, staffing, and anticipating busy or slow days. The measures provide insights into the consistency of patient flow and can support operational decisions to optimize efficiency and patient care quality.

References

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