Ch. 3 Vocab — Data Description

percentile formula

((number of values below X) + 0.5 / total number of values) * 100

percentile median

P-sub-50 (50th percentile)

quartile median

Q-sub-2 (50th percentile)

Mean

Sum of all the values divided by the number of values. This can either be a population ____ (denoted by mu) or a sample ____ (denoted by x bar)

Percentile

This divides the data set into 100 equal groups. The percent of the population which lies below that value. The data must be ranked to find this.

Sample Variance

Unbiased estimator of a population variance. Instead of dividing by the population size, the sum of the squares of the deviations from the sample mean is divided by one less than the sample size. The units on the variance are the units of the population squared.

Mild Outliers

Values which lie between 1.5 and 3.0 times the InterQuartile Range below the 1st Quartile or above the 3rd Quartile.

Extreme Outliers

Values which lie more than 3.0 times the InterQuartile Range below the 1st Quartile or above the 3rd Quartile.

percentile, percentage

A __________ is a relative measurement of position; whereas, a __________ is an absolute measure of the part to the total

Box and Whiskers Plot / Box Plot

A graphical representation of the minimum value, lower hinge, median, upper hinge, and maximum. Some textbooks define the five values as the minimum, first Quartile, median, third Quartile, and maximum.

Outlier

An extremely high or low value when compared to the rest of the values.

Parameter

Characteristic or measure obtained from a population

Statistic

Characteristic or measure obtained from a sample

data array

a data set that has been ordered

Quartile

a relative measure of position obtained by dividing the data set into quarters; either the 25th, 50th, or 75th percentiles, and the 50th percentile is called the median; divided into four groups

Decile

a relative measure of position obtained by dividing the data set into tenths; either the 10th, 20th, 30th, 40th, 50th, 60th, 70th, 80th, or 90th percentiles; divided into ten groups

Coefficient of Variation

allows one to compare standard deviations when the units are different; standard deviation divided by the mean expressed as a percentage

percentage

an absolute measure of the part to the total

range rule of thumb

an approximation of the standard deviation; the range is divided by 4

Five Number Summary

Minimum value, lower hinge, median, upper hinge, and maximum.

Empirical Rule / 68-95-99.7

Only valid when a distribution in bell-shaped (normal). Approximately 68% lies within 1 standard deviation of the mean; 95% within 2 standard deviations; and 99.7% within 3 standard deviations of the mean.

Greek letters

denote parameters (population)

Roman letters / Arabic letters

denote statistics (samples)

measures of variation

describes the distribution of data by showing how different each value is from the other; includes range, standard deviation, variance, and IQR

Standard Deviation

The square root of the variance. The population ________ _________ is the square root of the population variance, and the sample ________ _________ is the square root of the sample variance. The sample ________ _________ is not the unbiased estimator for the population standard deviation. The units on the ________ _________ is the same as the units of the population/sample.

population, sample

The __________ standard deviation is a parameter; whereas, the ______ standard deviation is a statistic.

measures of central tendency

lets us know what is normal or "average" for a set of data by condensing the data set down to one representative value; includes mean, median, mode, and midrange

negatively skewed distribution / left-skewed distribution

the majority of the data values fall to the right of the mean and cluster at the upper end of the distribution; the "tail" is to the left

multimodal

more than two modes

no mode

no data value is repeated

unimodal

one mode

symmetric distribution

the data values are evenly distributed on both sides of the mean; in a _________ ___________, the mean is the median.

positively skewed distribution / right-skewed distribution

the majority of data values fall to the left of the mean and cluster at the lower end of the distribution; the "tail" is to the right

percentile rank / percentile

the percentage of data values that fall below the specific rank

bimodal

two modes

measures of position

used to locate the relative position of a data value in the data set; includes z-scores, percentiles, deciles, and quartiles

sample mean

x̅

population mean

μ

z-score / standard score

-tells how many standard deviations a data value is above or below the mean for a specific distribution of values -obtained by subtracting the mean and dividing by the standard deviation -when all values are transformed to their ________ _____s, the new mean (for Z) will be zero and the standard deviation will be one -lets you compare apples to oranges

Chebyshev's Theorem

1-(1/k^2), when k>1; states the proportion of data values that fall k standard deviations of the mean. It can be applied to any distribution regardless of its shape.

decile median

D-sub-5 (50th percentile)

Population Variance

The average of the squares of the distances from the population mean. It is the sum of the squares of the deviations from the mean divided by the population size. The units on the variance are the units of the population squared.

Interquartile Range / IQR

The difference between the 3rd and 1st Quartiles.

Range

The difference between the highest and lowest values. Max - Min

Midrange

The mean of the highest and lowest values. (Max + Min) / 2

Weighted Mean

The mean when each value is multiplied by its weight and summed. This sum is divided by the total of the weights.

Lower Hinge / Lower Quartile

The median of the lower half of the numbers (up to and including the median). The _____ _____ is the first Quartile unless the remainder when dividing the sample size by four is 3.

Upper Hinge / Upper Quartile

The median of the upper half of the numbers (including the median). The _____ _____ is the 3rd Quartile unless the remainder when dividing the sample size by four is 3.

Median

The midpoint of the data after being ranked (sorted in ascending order). There are as many numbers below the ______ as above the ______.

Mode

The most frequent number