Chapter 3 Numerically Summarized Data

Arithmetic mean

A variable is computed by adding all the values of the variable in the data set and dividing by the number of observations

Popular arithmetic mean

u is a parameter that is computed using all the individuals in a population

Sample arithmetic mean

x is a statistic that is computed using the sample data.

Median

variable is the value that lies in the middle of the data when arranged in ascending order

Resistant

extreme observations relative to the data do not affect its value substantially

Mode

the most frequent observation of the variable

Multimodal

If a data set has 3 or more values that occur with the highest frequency

Dispersion

The degree to which the data are spread out.

Range

Variable is the difference between the largest and smallest data values.

Deviation about the mean

For the ith observation is x-u

Population Standard deviation

Square root of the sum of squared deviations about the population mean divided by the number of observations, N.

Sample Standard deviation

s a vairable is the square root of the sum of squared deviations about the sample mean divided by the n - 1,where n is the sample size.

Degrees of freedom

n - 1

Population variance

Square of the population standard deviation. Denoted by o²

Sample Variance

Square of the sample of the sample standard deviation and is denoted s².

Biased Statistic

Whenever a statistic consistently underestimates or overestimates a parameter, it is said to be bised.

Weighted Mean

X w of a variable is found by multiplying each value of the variable by its corresponding weight, adding these products, and dividing this sum by the sum of the weights

Z-score

The distance that a data value is from the mean in terms of the number of standard deviations.

Kth percentile

Denoted Pk of a data set is a value such that k percent of the observations are less than or equal to the value

Quartiles

Quartiles divide data sets into fourths

IQR

the range of the middle 50% of the observation in a data set.

Describe the distribution

describe its shape (skewed left, skewed right, or symmetric), its center (mean or median), and its spread (standard deviation or interquartile range)

Outliers

Extreme observations in a data set

Fences

serve as cutoff points for determining outliers

Five-number summary

a set of data consists of the smallest data value, Q1, the median, Q3, and the largest data value.

Whiskers

lines drawn from Q1 to the smallest data value that is larger than the lower fence and from Q3 to the largest data value that is smaller than the upper fence in a boxplot