What is the mean of a data set?

The mean, often referred to as the average, is calculated by adding all the values in the data set and then dividing by the number of values. For example, for the data set {2, 4, 6}, the mean is (2 + 4 + 6) / 3 = 4.

How do you calculate the median of a data set?

The median is the middle value of a data set when it is ordered from least to greatest. If there is an odd number of values, the median is the middle one. If there is an even number, it is the average of the two middle numbers. For example, in {1, 3, 3, 6, 7, 8, 9}, the median is 6; in {1, 2, 3, 4}, the median is (2 + 3) / 2 = 2.5.

What is the mode in a data set?

The mode is the value that appears most frequently in a data set. A data set can have one mode, more than one mode, or no mode at all. For example, in {1, 2, 2, 3, 4}, the mode is 2; in {1, 1, 2, 2}, both 1 and 2 are modes (bimodal); and in {1, 2, 3}, there is no mode.

What is standard deviation and what does it indicate?

Standard deviation is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range. It is calculated as the square root of the variance.

Define variance in the context of a data set.

Variance is a measure of how much the values in a data set differ from the mean. It is calculated as the average of the squared differences from the mean. For a sample, the formula is variance = Σ(x - mean)² / (n - 1), where n is the number of values.

What is a frequency distribution?

A frequency distribution is a summary of how often each value occurs in a data set. It can be represented in a table or a graph, showing the counts of occurrences for each value or range of values.

Explain the difference between population and sample statistics.

Population statistics refer to values derived from an entire population, while sample statistics refer to values derived from a subset of the population. Sample statistics are often used to estimate population parameters due to practical constraints.

What is the range of a data set and how is it calculated?

The range is the difference between the highest and lowest values in a data set. It is calculated as range = maximum value - minimum value. For example, in the data set {3, 7, 2, 9}, the range is 9 - 2 = 7.

If a data set has values {4, 8, 6, 5, 3}, what is the mode?

In the data set {4, 8, 6, 5, 3}, each value appears only once, which means there is no mode. A mode exists only if at least one value appears more than once.

What is the interquartile range (IQR) and how is it calculated?

The interquartile range (IQR) is a measure of statistical dispersion and is calculated as IQR = Q3 - Q1, where Q1 is the first quartile and Q3 is the third quartile. It represents the range of the middle 50% of the data.

In a normal distribution, what are the properties of the mean, median, and mode?

In a normal distribution, the mean, median, and mode are all equal and located at the center of the distribution. This symmetry indicates that the data is evenly distributed around the mean.