1
To solve for the quartile deviation, first calculate the first quartile (Q1) and the third quartile (Q3) of your data set. The quartile deviation is then found using the formula: ( \text{Quartile Deviation} = \frac{Q3 - Q1}{2} ). This value represents the spread of the middle 50% of your data, providing a measure of variability.
(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
(q3-q1)/2
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.
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.
The mean absolute deviation is 5
standard deviation is the square roots of variance, a measure of spread or variability of data . it is given by (variance)^1/2
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