1
(q3-q1)/2
(q3-q1)/2
procedure: step 1: arrange your raw data in increasing order. step 2: find the Q1 is the size of the (n+1)/4th value. step 3: find the Q3 is the size of the 3(n+1)/4th value. Quartile Deviation(QD)= (Q3-Q1)/2 for example: 87 ,64,74,13,19,27,60,51,53,29,47 is the given data step 1: 13,19,27,29,47,51,53,60,64,74,87 step 2: (n+1)/4=3 therefore Q1=27 step 3: 3(n+1)/4=9 therefore Q3=6 implies QD=18.5
Consider the data: 1, 2, 2, 3, 4, 4, 5, 7, 11, 13 , 19 (arranged in ascending order) Minimum: 1 Maximum: 19 Range = Maximum - Minimum = 19 - 1 = 18 Median = 4 (the middle value) 1st Quartile/Lower Quartile = 2 (the middle/median of the data below the median which is 4) 3rd Quartile/Upper Quartile = 11 (the middle/median of the data above the median which is 4) InterQuartile Range (IQR) = 3rd Quartile - 1st Quartile = 11 - 2 = 9
It is not possible to answer without any information on the spread (range, inter-quartile range, mean absolute deviation, standard deviation or variance).
Inter quartile range: quartiles are data items 1/4, 1/2 and 3/4 through a sorted list:232529 < Quartile 1313435 < Quartile 2 (Median)363738 < Quartile 34042InterQuartile range is Quartile 3 - Quartile 1; In this case, 38-29= 9It is a measure of how data is spread.How to calculate from mean and standard devation:mean = ustd. dev = sLook up .2465 in the z-table as 24.65% of the data lies to the left of Q1 and you will find z = -0.7.You know s and u, so solve for x.z = (x-u)/sx = u + sz24.65% of the data lies to the right of Q2. So look up the z-value for 1 - 0.2465, repeat.
The mean absolute deviation is 5
Rank them from highest to lowest. The lowest 25 percent of them represent the bottom quartile. Let's say you have the following data set: 1, 8, 2, 7, 3, 6, 4, 5 Rank them thus: 1, 2, 3, 4, 5, 6, 7, 8 Twenty-five percent of eight (the number of data points) is two. Therefore, the bottom two data points (1 and 2) represent the bottom quartile.
standard deviation is the square roots of variance, a measure of spread or variability of data . it is given by (variance)^1/2
Mean is 3.8 Mean Absolute Deviation is 1.44
Step 1: Find the upper quartile, Q3.Step 2: Find the lower quartile: Q1.Step 3: Calculate IQR = Q3 - Q1.Step 1: Find the upper quartile, Q3.Step 2: Find the lower quartile: Q1.Step 3: Calculate IQR = Q3 - Q1.Step 1: Find the upper quartile, Q3.Step 2: Find the lower quartile: Q1.Step 3: Calculate IQR = Q3 - Q1.Step 1: Find the upper quartile, Q3.Step 2: Find the lower quartile: Q1.Step 3: Calculate IQR = Q3 - Q1.
4.55% falls outside the mean at 2 standard deviation