Flash Cards: Statistics

Statistics is the science of collecting, analyzing, interpreting, and presenting data.

The three measures of central tendency are Mean, Median, and Mode.

If n (number of observations) is odd, median is the ((n + 1) / 2)th observation. If n is even, median is the mean of the (n/2)th and (n/2 + 1)th observations.

Range = Maximum value - Minimum value of the data set.

To understand how data points are spread out or clustered around a central tendency.

Mean deviation is the average of the absolute deviations of data points from a central value.

M.D.(a) = (Σ |xᵢ - a|) / n, where a is the central value and n is the number of observations.

Standard deviation (σ) measures the amount of variation or dispersion of a set of values.

σ = √(Σ(xᵢ - x̄)² / n) where x̄ is the mean.

Mean = (6 + 7 + 10 + 12) / 4 = 8.75.

Mean considers all values, while median is the middle value that keeps half data below and half above.

A larger range indicates greater variability or dispersion in the data.

Mean deviation may not be reliable for datasets with high variability or outliers.

Cumulative frequency is the sum of the frequencies of all previous classes in a frequency distribution.

It helps assess the risk and variability in various fields, such as finance and quality control.

Quartile deviation is a measure of spread that accounts for the middle 50% of data.

Outliers can skew the mean, making it less representative of the data compared to the median.

A normal distribution is a bell-shaped curve where most observations cluster around the central peak.