Question

The data below shows the daily number of cars that passes through a roundabout for some randomly selected days. 43 21 9 33 15 33 49 18 28 46 25 40 32 58 20 25 24 25 62 38 20 What is the quartile deviation is

Answer 1

Answer:

Step-by-step explanation:this is answer

Answer 2

$Given \:data : \\43,21,9,33,15, \\33,49,18,28,46,\\25,40,32,58,20,\\25,24,25,62,38,\\20$

$Number \:of \: items = n$

/* Arranging the data in ascending order , we get */

$9,15,18,20,20, \\21,24,25,25,25,\\28,32,33,33,38,\\40,43,46,49,58,\\62$

$\blue{Q_{1} }= Value \:of \: \Big( \frac{n+1}{4}\Big)^{th}\: item \\= Value \:of \: \Big(\frac{21+1}{4}\Big) ^{th} \:item \\= Value \: \Big(\frac{22}{4}\Big)^{th} \:item \\= 5.5 \\= 5^{th} \:item + 0.5 \\= (6^{th} \:item - 5^{th} \:item ) \\= 21 - 20 \\= 1$

$\pink { Q_{3}} = Value \:of \: \Big( \frac{3(n+1)}{4}\Big)^{th}\: item \\= Value \:of \: \Big(\frac{3(21+1)}{4}\Big) ^{th} \:item \\= Value \: \Big(\frac{3\times 22}{4}\Big)^{th} \:item \\= 3 \times 5.5\\= 16.5 \:item \\= 16.5^{th} \:item + 0.5 \\= (16^{th} \:item - 17^{th} \:item ) \\= 43 - 40 \\= 3$

$Now, \red{Quartile \: Deviation (Q.D) }= \frac{Q_{3}-Q_{1}}{2} \\= \frac{3-1}{2} \\= \frac{2}{2} \\= 1$

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