Measures of Dispersion Examples
Введение:
Measures of dispersion are statistical tools used to understand the spread or variability of a dataset. They provide valuable information about the extent to which the values in a dataset deviate from the mean or central tendency. В этой статье, we will explore various measures of dispersion and provide examples to enhance your understanding.
я. Диапазон:
The range is the simplest measure of dispersion and is calculated by subtracting the smallest value from the largest value in a dataset. Например, let’s consider the heights (in centimeters) of five individuals: 160, 165, 170, 175, и 180. The range would be 180 – 160 "=" 20, indicating that the height values vary by 20 centimeters.
II. Interquartile Range (IQR):
The interquartile range measures the spread of the middle 50% of the data and is calculated by subtracting the lower quartile (Q1) from the upper quartile (Q3). Например, let’s consider the scores obtained by a group of students in a test: 60, 65, 70, 75, 80, 85, 90. The lower quartile would be the median of the lower half of the dataset (Q1 = 65), and the upper quartile would be the median of the upper half (Q3 = 85). Поэтому, the IQR is 85 – 65 "=" 20, indicating that the scores of the students in the middle range vary by 20.
III. Дисперсия:
Variance measures the average squared deviation of each data point from the mean. It gives a more comprehensive understanding of the spread compared to the range. Consider a dataset representing the number of cars sold per day in a week: 50, 60, 40, 70, 45. The mean of this dataset is (50+60+40+70+45)/5 "=" 53. The variance is calculated as the sum of squared deviations from the mean, divided by the total number of data points. В этом случае, it would be ((50-53)^2+(60-53)^2+(40-53)^2+(70-53)^2+(45-53)^2)/5 "=" 130.4.
IV. Среднеквадратичное отклонение:
The standard deviation is the square root of variance, and it provides a more interpretable measure of dispersion. Continuing with the previous example, the standard deviation would be the square root of the variance, making it approximately 11.42.
Заключение:
Measures of dispersion play a crucial role in descriptive statistics by quantifying the spread or variability of datasets. В этой статье, we explored several examples, including the range, interquartile range, дисперсия, и стандартное отклонение. Understanding these measures will enable researchers and analysts to make more informed decisions and gain comprehensive insights from their data.
