Question

Number	January	July
1	100	136
2	190	235
3	125	97
4	610	179
5	260	156
6	167	200
7	255	219
8	205	400
9	256	86
10	330	215
11	460	125
12	242	133
13	220	199
14	140	210
15	158	255
16	130	148
17	144	210
18	176	126
19	220	120
20	231	285
21	160	202
22	315	218
23	143	90
24	340	144
25	200	180

• Compute the quartiles for each sample period and determine if there are any outliers

Answer 1

solution:

From the given data

1) Let's arrange the sample period for january in ascending order

  [ 100, 125 , 130 , 140 , 143 , 144 , 158 , 160 , 167 , 176 , 190 , 200 , 205 , 220 , 220 , 231 , 242 , 255 , 256 , 260 , 315 , 330 , 340 , 460 , 610 ]

Total no.of samples (n) = 25

i) First quartile (Q1)

  First quartile (Q1) = 25% of data

= 0.25 * (n+1) th term

= 0.25 * 26 th term

= 6.5 th term

= Average of 6th and 7th terms

= (144+158) / 2

= 151

ii) Second quartile (Q2) or Median

Median (Q2) = (n+1)/2 th term [ since n is odd ]

= 26/2 th term

= 13th term

= 205

iii) Third quartile (Q3)

Third quartile (Q3) = 75% of data

= 0.75 * (n+1) th term

= 0.75 * 26 th term

= 19.5 th term

= Average of 19th and 20th terms

= (256+260) / 2

= 258

Here, Inter quartile Range (IQR) = Q3 - Q1 = 258 - 151 = 107

Outliers : outliers are the values which are out of range of (Q1-1.5 (IQR) , Q3+1.5 (IQR) )

   ( 151 - 160.5 , 258 + 160.5)

( -9.5 , 418.5)

Therefore , 460 and 610 are outliers present in january period

2) Let's arrange the sample period for july in ascending order

  [ 86 , 90 , 97 , 120 , 125 , 126 , 133 , 136 , 144 , 148 , 156 , 179 , 180 , 199 , 200 , 202 , 210 , 210 , 215 , 218 , 219 , 235 , 255 , 285 , 400 ]

Total no.of samples (n) = 25

i) First quartile (Q1)

  First quartile (Q1) = 25% of data

= 0.25 * (n+1) th term

= 0.25 * 26 th term

= 6.5 th term

= Average of 6th and 7th terms

= (126+133) / 2

= 129.5

ii) Second quartile (Q2) or Median

Median (Q2) = (n+1)/2 th term [ since n is odd ]

= 26/2 th term

= 13th term

= 180

iii) Third quartile (Q3)

Third quartile (Q3) = 75% of data

= 0.75 * (n+1) th term

= 0.75 * 26 th term

= 19.5 th term

= Average of 19th and 20th terms

= (215+218) / 2

= 216.5

Here, Inter quartile Range (IQR) = Q3 - Q1 = 216.5 - 129.5 = 87

Outliers : outliers are the values which are out of range of (Q1-1.5 (IQR) , Q3+1.5 (IQR) )

   ( 129.5 - 130.5 , 216.5 + 130.5)

( 1 , 347)

Therefore , 400 is  the outlier in july period