Question

Произвести первичную обработку данных: В течение года результаты заплывов спортсменки Сомовой фиксировались на карточках. За год набралось 500 карточек. Выяснить основные статистические характеристики результатов заплывов Сомовой, используя следующую выборку: 14,1; 16,5; 15,9; 14,9; 15,7; 16,5; 15,9; 14,9; 15,7;15,6; 15,9.

Answer 1

54 54 65 765 867 32 4324 7567 5423 45435 654654 54354 5435 

Answer 2

Primary Data Processing: Analyzing Swim Results

To analyze the swim results of athlete Svetlana Somova, we will calculate the main statistical characteristics using the given sample data. The sample data consists of 11 swim times recorded on cards over the course of a year. The swim times are as follows: 14.1, 16.5, 15.9, 14.9, 15.7, 16.5, 15.9, 14.9, 15.7, 15.6, and 15.9.

Mean

The mean, also known as the average, is a measure of central tendency that represents the sum of all values divided by the number of values. To calculate the mean swim time for Svetlana Somova, we add up all the swim times and divide by the total number of times:

(14.1 + 16.5 + 15.9 + 14.9 + 15.7 + 16.5 + 15.9 + 14.9 + 15.7 + 15.6 + 15.9) / 11 = 15.1

Therefore, the mean swim time for Svetlana Somova is 15.1 seconds.

Median

The median is another measure of central tendency that represents the middle value when the data is arranged in ascending or descending order. To calculate the median swim time for Svetlana Somova, we first arrange the swim times in ascending order:

14.1, 14.9, 14.9, 15.6, 15.7, 15.7, 15.9, 15.9, 15.9, 16.5, 16.5

Since there are 11 swim times, the median will be the value in the middle, which is the 6th value:

Median swim time: 15.7 seconds

Mode

The mode is the value that appears most frequently in a dataset. In the given swim times, there is no value that appears more than once. Therefore, there is no mode in this dataset.

Range

The range is the difference between the maximum and minimum values in a dataset. To calculate the range of swim times for Svetlana Somova, we subtract the minimum value from the maximum value:

Maximum swim time: 16.5 seconds Minimum swim time: 14.1 seconds

Range of swim times: 16.5 - 14.1 = 2.4 seconds

Variance

Variance measures the spread or dispersion of the data points from the mean. To calculate the variance of the swim times for Svetlana Somova, we use the following formula:

Variance = (Σ(x - μ)²) / n

Where: - Σ represents the sum of the squared differences between each value (x) and the mean (μ). - n represents the total number of values.

First, we calculate the squared differences between each swim time and the mean:

(14.1 - 15.1)² + (16.5 - 15.1)² + (15.9 - 15.1)² + (14.9 - 15.1)² + (15.7 - 15.1)² + (16.5 - 15.1)² + (15.9 - 15.1)² + (14.9 - 15.1)² + (15.7 - 15.1)² + (15.6 - 15.1)² + (15.9 - 15.1)²

Next, we sum up these squared differences:

(0.1)² + (1.4)² + (0.8)² + (0.2)² + (0.6)² + (1.4)² + (0.8)² + (0.2)² + (0.6)² + (0.5)² + (0.8)² = 3.74

Finally, we divide the sum by the total number of values:

Variance = 3.74 / 11 = 0.34

Therefore, the variance of the swim times for Svetlana Somova is 0.34 seconds squared.

Standard Deviation

The standard deviation is the square root of the variance and provides a measure of the spread or dispersion of the data points. To calculate the standard deviation of the swim times for Svetlana Somova, we take the square root of the variance:

Standard Deviation = √0.34 = 0.58

Therefore, the standard deviation of the swim times for Svetlana Somova is 0.58 seconds.

Conclusion

Based on the given sample data, the main statistical characteristics of Svetlana Somova's swim results are as follows: - Mean swim time: 15.1 seconds - Median swim time: 15.7 seconds - Range of swim times: 2.4 seconds - Variance: 0.34 seconds squared - Standard deviation: 0.58 seconds

Please note that these calculations are based on the provided sample data and may not represent the complete set of swim results for Svetlana Somova.