Use the data below to answer each of the following questions: 192    228    186    199    238    217    213    234    264    187    214    115    238    246   Min:   Q1:   Median:   Q3:   Max:   IQR:  

• Min : 115 
• Q1 : 192
• Median : 215.5
• Q3 : 238
• Max : 264 
• IQR : 46

Step-by-step explanation

Given data is, 

192  ,  228 ,   186 ,   199   , 238  ,  217 ,   213 ,   234 ,   264 ,   187 ,   214 ,   115 ,   238 ,   246

We arrange the data in ascending order and give observation numbers (rankings)

From the data we observe that, 

• Min : 115 
• Max : = 264
• 1st quartile :- 

We know that, 

The 1st quartile is the median of the lower half data 

That is, 

The 1st quartile is the median of 1st 7 Observations 

By the definition, 

Q1?=Medianoflowerhalfdata=(27+1?)thobservation?Q1?=4thobservation?Q1?=192

• Median :- 

In this case we can see that,  n = 14 

Median=2(2n?)thobservation+(2n?+1)thobservation??Median=2(214?)thobservation+(214?+1)thobservation??Median=27thobservation+8thobservation??Median=2214+217??Median=215.5

• 3rd quartile :- 

We know that, 

The 2nd quartile is the median of the upper half data 

That is, 

The 2nd quartile is the median of 2nd  7 Observations 

By the definition, 

Q3?=MedianofUpperhalfdata=(27+1?)thobservation?Q3?=4thobservation?Q3?=238

• IQR :- 

We know that, 

IQR=Q3?−Q1??IQR=238−192?IQR=46