Describing Quantitative Data with Numbers

Mean

the average of all the individual data values. To find the mean, add all the values and divide by the total number of data values; given by the formula x bar = sum of data values/number of data values

Statistic

number that describes some characteristic of a sample

Parameter

a number that describes some characteristic of a population

Resistant

a measure is resistant if it isn’t sensitive to extreme values

Median

the midpoint of a distribution, the number such that about half of the observations are smaller and about half are larger; if the n of data values is odd, the median is the middle value in the ordered list, if the number of n data values is even, use the average of the two middle values in the ordered list

Range

the distance between the minimum value and the maximum value; Range = Maximum - Minimum

Standard Deviation

measures the typical distance of the values in a distribution from the mean; calculated by finding an average of the squared deviations and then taking the squared root

Variance

the average squared deviation

Quartiles

divide the ordered data set into four groups having roughly the same number of values

First Quartile (Q1)

the median of the data values that are to the left of the median in the ordered list

Third Quartile (Q3)

the median of the data values that are to the right of the median in the ordered list

Interquartile range (IQR)

the distance between the first and third quartile of a distribution; IQR = Q3 - Q1

Five-number summary

consists of the minimum, the first quartile (Q1), the median, the third quartile (Q3), and the maximum

Boxplot

a visual representation of the five-number summary