Questions: 2 1 6 4 1 2 3 2 2 3 5 1 5 2 6 5 1 2 1 2 4 4 3 6 6 2 5 2 4 2 4 3 4 3 2 2 4 6 5 1 2 5 6 5 1 5 3 2 1 1

Solution Steps

To solve the problem, we need to calculate the mean, median, and mode of the given numbers. The mean is the average of all numbers, the median is the middle value when the numbers are sorted, and the mode is the number that appears most frequently. We will also calculate the standard deviation, which measures the amount of variation or dispersion in the set of numbers.

1. Mean: Sum all the numbers and divide by the count of numbers.
2. Median: Sort the numbers and find the middle value. If the count of numbers is even, the median is the average of the two middle numbers.
3. Mode: Identify the number that appears most frequently in the list.
4. Standard Deviation: Calculate the square root of the average of the squared differences from the mean.

The mean \( \mu \) is calculated using the formula: \[ \mu = \frac{\sum x_i}{n} \] where \( \sum x_i \) is the sum of all numbers and \( n \) is the count of numbers. For the given data, the mean is: \[ \mu = 3.18 \]

The median is the middle value of the sorted data. If the number of observations \( n \) is odd, the median is the middle number; if \( n \) is even, it is the average of the two middle numbers. In this case, the median is: \[ \text{Median} = 3.0 \]

The mode is the number that appears most frequently in the dataset. For the given numbers, the mode is: \[ \text{Mode} = 2 \]

The standard deviation \( \sigma \) is calculated using the formula: \[ \sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{n - 1}} \] For the dataset, the standard deviation is: \[ \sigma \approx 1.6986 \]

Final Answer