Elementary Statistics Ch.3 Data Description Flashcards | Quizlet

Descriptive Statistics

Methods used to summarize, organize, and describe data, such as measures of average, variation, and position.

Measures of Central Tendency

Measures that determine the center or most typical case of a distribution, including the mean, median, mode, and midrange.

Measures of Variation

Measures that determine the spread or dispersion of data values, including the range, variance, and standard deviation.

Measures of Position

Measures that indicate the relative position of a data value in a set, such as percentiles, deciles, quartiles, and z scores.

Statistic

A characteristic or measure obtained by using the data values from a sample.

Parameter

A characteristic or measure obtained by using all the data values from a specific population.

General Rounding Rule for Statistics

Do not round during intermediate calculation steps; round only the final answer.

Arithmetic Mean

The sum of the values divided by the total number of values.

Rounding Rule for the Mean

Round the mean to one more decimal place than occurs in the raw data.

Median

The midpoint (halfway point) of a data array arranged in ascending order.

Mode

The value that occurs most often in a data set.

Midrange

The sum of the lowest and highest values in a data set divided by $2$.

Weighted Mean

A mean used when values are not all equally represented, calculated by multiplying each value by its weight and dividing by the sum of the weights.

Positively Skewed (Right-Skewed) Distribution

A distribution where the majority of data values fall to the left, and the tail is to the right.

Negatively Skewed (Left-Skewed) Distribution

A distribution where the majority of data values fall to the right, and the tail is to the left.

Symmetric Distribution

A distribution where data values are evenly distributed on both sides of the mean, and mean, median, and mode are equal.

Range

The highest value minus the lowest value in a data set.

Population Variance

The average of the squares of the distance each value is from the mean, denoted by sigma squared ($\sigma^2$).

Population Standard Deviation

The square root of the population variance, denoted by sigma ($\sigma$).

Coefficient of Variation (CVar)

The standard deviation divided by the mean, expressed as a percentage, used to compare standard deviations with different units.

Range Rule of Thumb

A rough estimate of the standard deviation calculated by dividing the range by $4$ ($s \approx \frac{\text{Range}}{4}$).

Chebyshev's Theorem

A theorem stating that the proportion of values falling within $k$ standard deviations of the mean is at least $1 - \frac{1}{k^2}$ (for $k > 1$).

Empirical (Normal) Rule

For bell-shaped distributions: approximately $68\%$, $95\%$, and $99.7\%$ of data fall within $1$, $2$, and $3$ standard deviations of the mean, respectively.

Standard Score (z score)

A score telling how many standard deviations a data value is above or below the mean, calculated as (Value minus Mean) divided by Standard Deviation ($z = \frac{X - \mu}{\sigma}$).

Interquartile Range (IQR)

The difference between the third and first quartiles ($Q_3 - Q_1$).