Question

Use the accompanying data set to complete the following actions. a. Find the quartiles. b. Find the interquartile range. c. Identify any outliers. 41 53 37 44 40 36 39 47 43 39 34 56 42 36 15 51 39 50 29 29 0 a. Find the quartiles. The first quartile, Q7, is The second quartile, Q2, is The third quartile, Q3, is (Type integers or decimals.) b. Find the interquartile range. The interquartile range (IQR) is (Type an integer or a decimal.) c. Identify any outliers. Choose the correct choice below. Click to select your answer(s).

Answer 1

The first quartile Q_{^{​​​​​​}​​​​​​1}​​ is 36

The second quartile  Q_{^{​​​​​​}​​​​​2} is 39.5

The third quartile Q_{^{​​​​​​}​​​​​​3} is 46.25

Inter quartile range is

IQR is 10.25

The outlier is 15

The given data is (x): 41, 53, 37, 44, 49,36, 39, 47,43, 39, 34,56, 42, 36, 15, 51, 39,50, 29, 29 Arronging data in Ascending order 15, 29, 29, 34,36, 36, 37, 39, 39, 39, 40, 41, 42,43,44,47 50, 51, 53, 56 _Heresample size D = 20 is even The firs quortite (Q) iš computed as Que size of Cotthobservation size of ( 20+13th Observation 5 size of (5.25th obosey votion = size of Sthabs +0.25 Loth_sthaben) = 36+ 0.25 (36-36) = 36

The second quartile (Q2) is 12 = mediane size of ( nti thobne size of Clousyth Olsh 22 = size of 10 th obsn 70.5(lith-10th obsn) las = 39+0.5(40-39) = 39.5 The Third quartile @) is ez=size of 3(+1) thosh= sizeof (3.120+1)) thabsh = size of (15.75 theobsn= size of is thods+0.75618th-istholss) Q3 = 44+0.75 (47-44) = 46.25 the inter quartile yonge (IPR) is IQR=23-2= 46.25-36=10.25

Now we cop compute the lower and upper limit for outliers Howey R-1:5XIPR= 36-1.5X10.25 = 20:625 tupper = R3+ los Xter=46:25 Hº5X10.25 = 61.625 Land then observation X is an outlier if X 2 20.625 x Litx765.625 L In this case, there is one outlion in the do to and Lthe outlier-is 15 because Is is the observation which Loot greater then 20.625 le lower limit for outlier.