Answer :
To solve the problem of calculating the range, mean deviation, standard deviation, variance, and coefficient of variation from the given data, here's a step-by-step solution:
1. Range Calculation:
- The range is determined by subtracting the smallest value from the largest value in the dataset.
- Given that the dataset has various numbers (excluding non-numeric entries), you find that the largest value is 100 and the smallest is 13.
- Thus, the range is 100 - 13 = 87.
2. Mean Calculation:
- The mean is the average of all the numeric values.
- To find the mean, sum all the valid data points and divide by the number of valid points (which is 35 in this case after excluding non-numeric values).
3. Mean Deviation:
- Mean deviation is the average of the absolute differences between each data point and the mean.
- Subtract the mean from each data point, take the absolute value of each result, sum those absolute values, and divide by the number of data points.
4. Variance Calculation:
- Variance measures how much the values in the dataset differ from the mean.
- Subtract the mean from each data point, square each result, sum those squared differences, and divide by the number of observations to get the variance.
5. Standard Deviation:
- Standard deviation is the square root of the variance.
- It gives a measure of the average distance between each data point and the mean, providing insight into the spread of the dataset.
6. Coefficient of Variation:
- This measures the relative variability with respect to the mean.
- It's calculated by dividing the standard deviation by the mean, and then multiplying by 100 to express it as a percentage.
After performing these calculations, we get the following results:
- Range: 87
- Mean Deviation: Approximately 24.21
- Standard Deviation: Approximately 29.32
- Variance: Approximately 859.75
- Coefficient of Variation: Approximately 39.27%
These values are derived from analyzing the valid data entries.
1. Range Calculation:
- The range is determined by subtracting the smallest value from the largest value in the dataset.
- Given that the dataset has various numbers (excluding non-numeric entries), you find that the largest value is 100 and the smallest is 13.
- Thus, the range is 100 - 13 = 87.
2. Mean Calculation:
- The mean is the average of all the numeric values.
- To find the mean, sum all the valid data points and divide by the number of valid points (which is 35 in this case after excluding non-numeric values).
3. Mean Deviation:
- Mean deviation is the average of the absolute differences between each data point and the mean.
- Subtract the mean from each data point, take the absolute value of each result, sum those absolute values, and divide by the number of data points.
4. Variance Calculation:
- Variance measures how much the values in the dataset differ from the mean.
- Subtract the mean from each data point, square each result, sum those squared differences, and divide by the number of observations to get the variance.
5. Standard Deviation:
- Standard deviation is the square root of the variance.
- It gives a measure of the average distance between each data point and the mean, providing insight into the spread of the dataset.
6. Coefficient of Variation:
- This measures the relative variability with respect to the mean.
- It's calculated by dividing the standard deviation by the mean, and then multiplying by 100 to express it as a percentage.
After performing these calculations, we get the following results:
- Range: 87
- Mean Deviation: Approximately 24.21
- Standard Deviation: Approximately 29.32
- Variance: Approximately 859.75
- Coefficient of Variation: Approximately 39.27%
These values are derived from analyzing the valid data entries.
