Statistics 3.4

Interquartile range

The ... IQR, is the range of the middle 50% of the observations in a data set. That is, the IQR is the difference between the third and first quartiles and is found using the formula

z-scores

... Represents the distance that a data value is from the mean in terms of the number of standard deviations. We find it by subtracting the mean from the data value and dividing this result by the standard deviation

Quartiles

This divides data sets into fourths, or four equal parts.

population z-score

M = Mean O = Standard Deviation

Finding Quartiles

Step 1 Arrange the data in ascending order. Step 2 Determine the median, M, or second quartile, Q2 . Step 3 Divide the data set into halves: the observations below (to the left of) M and the observations above M. The first quartile, Q1 , is the median of the bottom half, and the third quartile, Q3 , is the median of the top half.

Checking for Outliers by Using Quartiles

Step 1 Determine the first and third quartiles of the data. Step 2 Compute the interquartile range. Step 3 Determine the fences. Fences serve as cutoff points for determining outliers. Lower Fence = Q1 - 1.5(IQR) Upper Fence = Q3 + 1.5(IQR) Step 4 If a data value is less than the lower fence or greater than the upper fence, it is considered an outlier.

kth percentile

The ... denoted, Pk , of a set of data is a value such that k percent of the observations are less than or equal to the value.

Q1 Q2 Q3

The 1st quartile, denoted Q1, divides the bottom 25% the data from the top 75%. Therefore, the 1st quartile is equivalent to the 25th percentile. The 2nd quartile divides the bottom 50% of the data from the top 50% of the data, so that the 2nd quartile is equivalent to the 50th percentile, which is equivalent to the median. The 3rd quartile divides the bottom 75% of the data from the top 25% of the data, so that the 3rd quartile is equivalent to the 75th percentile.

unitless

The z-score is ... It has mean 0 and standard deviation 1.