• 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)

Rank (Observation number )	1	2	3	4	5	6	7	8	9	10	11	12	13	14
Observation	115	186	187	192	199	213	214	217	228	234	238	238	246	264

 

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 

Rank (Observation number )	1	2	3	4	5	6	7
Observation	115	186	187	192	199	213	214

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 

Rank (Observation number )	1	2	3	4	5	6	7
Observation	217	228	234	238	238	246	264

By the definition, 

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

 

• IQR :- 

We know that, 

IQR=Q3?−Q1??IQR=238−192?IQR=46