Statistics Assessment

5 Number Summary

Consists of the minimum value, 1st quartile, median, 3rd quartile, and the maximum value of a data set.

3rd/Upper Quartile

Quartile that is greater than the median. Separates the data greater than the median into two equal parts. 75% of the data is below the third quartile and 25% of the data is above the third quartile.

Median

Separates the data into 2 equal parts. 50% of the data is below the median and 50% of the data is above the median.

About ____% of the values are within one standard deviation from the mean.

68

About ____% of the values are within two standard deviations from the mean.

95

About ____% of the values are within three standard deviations from the mean.

99.7

Mean

A calculated "central" value of a set of numbers. To calculate, just add up all the numbers, then divide by how many numbers there are.

Outliar

Any value in a set of data that is at least 1.5 interquartile ranges beyond the upper or lower quartile. An extreme value.

Skewed Left/Negatively Skewed

Fewer data plots are found to the left of the graph toward smaller numeric values. The "tail" of the graph is pulled toward the lower positive numbers, or negative numbers, or to the left. The mean typically gets pulled toward the tail and is less than the median.

Skewed Right/Positively Skewed

Fewer data plots are found to the right of the graph toward the larger numeric values. The "tail" of the graph is pulled toward the higher positive numbers, or to the right. The mean typically gets pulled toward the tail and is greater than the median.

Normal Distribution

When graphed, a vertical line drawn at the center will produce mirror images with the left half of the graph being the mirror image of the right. Produces the typical "bell" shape or bell curve. Highest vertical column is typically in the center.

Standard Deviation

It is a measure of the dispersion of a set of data from its mean. The more spread apart the data, the higher the deviation. Standard deviation is calculated as the square root of variance.

Variance

It measures how far each number in the set is from the mean. It is calculated by taking the differences between each number in the set and the mean, squaring the differences, and dividing the sum of the squares by the number of values in the set.

1st/Lower Quartile

Quartile that is less than the median. Separates the data below the median into two equal parts. 25% of the data is below the first quartile and 75% is above the first quartile.

What is the relationship between the mean and the median for negatively skewed data?

mean < median

What is the relationship between the mean and the median for uniform distribution?

mean = median

What is the relationship between the mean, median, and mode for normal distribution?

mean = median = mode

What is the relationship between the mean and the median for positively skewed data?

mean > median

Mode

The value that appears most often in a set of data.

Standard Deviation Formula

σ= square root of (Σ ( x - x̅ )^2 / N)

Variance Formula

σ^2 = Σ ( x - x̅ )^2 / N

Properties of normal distributions

- Graph is maximized at the mean - The total area under the curve is equal to 1 (or 100%) - The curve is symmetrical about the mean

Uniform Distribution

The data is spread equally across the range. Each data entry appears the same number of times in the set. Each section of the box plot is equal in length - min to first quartile, first quartile to median, median to third quartile and third quartile to maximum.

Interquartile Range (IQR)

The difference between the upper and lower quartiles