Final answer:
To calculate the mean, median, mode, variance, standard deviation, and range for the given dataset, add up all the values and divide by the total number of values to find the mean. Arrange the values in order and find the middle value to find the median. Determine the value that appears most frequently to find the mode. Subtract the mean from each value, square the result, and find the average of these squared differences to calculate variance. The standard deviation is the square root of the variance. The range is the difference between the highest and lowest values in the dataset. These measures can help in understanding the data distribution and drawing inferences about the dataset.
Step-by-step explanation:
Mean:
To calculate the mean, add up all the values in the dataset and divide by the total number of values. For example, for the Points column, the mean would be (3.9 + 3.9 + 7 + 3.08 + 3.15 + 2.76 + 3.21) / 7 = 29.1 / 7 =
4.157
Median:
To find the median, arrange the values in order from least to greatest and find the middle value. If there is an odd number of values, the median is the middle value. If there is an even number of values, the median is the average of the two middle values. For example, for the Score column, the median would be 3.215.
Mode:
The mode is the value that appears most frequently in the dataset. If there are multiple values that appear with the same highest frequency, the dataset is considered multimodal. For example, for the Weight column, the mode would be 17.02.
Variance:
To calculate the variance, subtract the mean from each value, square the result, and find the average of these squared differences. For example, for the Points column, the variance would be ((3.9 - 4.157)^2 + (3.9 - 4.157)^2 + (7 - 4.157)^2 + (3.08 - 4.157)^2 + (3.15 - 4.157)^2 + (2.76 - 4.157)^2 + (3.21 - 4.157)^2) / 7 = 1.064.
Standard Deviation:
The standard deviation is the square root of the variance and provides a measure of the spread or dispersion of the dataset. For example, for the Score column, the standard deviation would be the square root of the variance.
Range:
The range is the difference between the highest and lowest values in the dataset. For example, for the Points column, the range would be the difference between the maximum value and the minimum value.
Comment/Inferences:
Based on the calculated mean, median, mode, variance, standard deviation, and range, we can draw the following observations: The mean, median, and mode for each column provide insight into the central tendency and frequency of values. The variance and standard deviation indicate the degree of variability or spread in the dataset. The range gives an idea of the overall range of values. These measures can help in understanding the data distribution and drawing inferences about the dataset.