Final answer:
A single number used to represent a group of numbers is commonly known as the average, typically the arithmetic mean. In a symmetrical distribution, the mean, median, and mode are equal. Calculations of mean and standard deviation involve specific steps and depend on whether the distribution is skewed or not.
Step-by-step explanation:
A single number used to represent a group of numbers can be referred to as an average, which is a term that describes the central tendency of the data. There are several types of averages, such as the arithmetic mean, median, mode, weighted mean, and geometric mean. However, when people commonly refer to the average, they are usually talking about the arithmetic mean, which is calculated by adding all the values and dividing by the number of values.
In a symmetrical distribution, the mean, median, and mode are all the same. This is because a symmetrical distribution is perfectly balanced, and the central tendency can be accurately represented by any of these three measures. However, in cases where the data is skewed, the mean is influenced more by extreme values, compared to the median or mode.
To answer the specific questions:
- In a symmetrical distribution, the relationship among the mean, median, and mode is that they are all equal.
- To compute the mean and standard deviation for the given data (10; 11; 15; 15; 17; 22), the mean is the sum of the numbers divided by the count of numbers. The standard deviation is a measure of the amount of variation or dispersion of a set of values. A detailed calculation would involve finding the variance first by calculating the squared difference between each data point and the mean, summing these values, dividing by the number of values minus one, and then taking the square root of the variance to get the standard deviation.
- The number that is two standard deviations above the mean can be calculated by adding twice the standard deviation to the mean of the data.