Question

The lengths (in kilometers) of rivers on the South Island of New Zealand that flow to the Pacific Ocean are listed in table #3.3.13 (Lee, 1994). Table #3.3.13: Lengths of Rivers (km) Flowing to Pacific Ocean River Length (km) River Length (km) Clarence 209 Clutha 322 Conway 48 Taieri 288 Waiau 169 Shag 72 Hurunui 138 Kakanui 64 Waipara 64 Waitaki 209 Ashley 97 Waihao 64 Waimakariri 161 Pareora 56 Selwyn 95 Rangitata 121 Rakaia 145 Ophi 80 Ashburton 90 Find the five-number summary and interquartile range (IQR), and draw a boxand-whiskers plot

Answer 1

putting above in ascending order:

S. no	X
1	48
2	56
3	64
4	64
5	64
6	72
7	80
8	90
9	95
10	97
11	121
12	138
13	145
14	161
15	169
16	209
17	209
18	288
19	322

minimum =48

quartie 1 =(n+1)/4 th value =5h value =64

Quartile 2 (median) =(n+1)/2 th value =10th value =97

Quartile 3 =3(n+1)/4 th value =15th value =169

maximum=322

therefore below is 5 number summary:

48 , 64 ,97 ,169 ,322

interquartile rage =Q3-Q1 =169-64=105

below is  boxand-whiskers plot: