Question

This example was previously posted, but how did we come up with a Q1 result of 28.5 and a Q3 result of 123.3 for the question below? I am wondering where I went wrong here, as the results to this question have already been posted. The results I have are Q1 of 29 and Q3 of 121 with a median of 69. I have IQR as 92 and for outliers I have -109 for lower limit and 259 for upper limit. I am wondering how we came up with 28.5 for Q1 and 123.3 for Q3. Once I understand this, then figuring out IQR and outlier limits makes sense.

Hospital - Infections

1	89
2	58
3	96
4	206
5	31
6	16
7	249
8	79
9	29
10	6
11	222
12	108
13	58
14	54
15	81
16	64
17	9
18	130
19	37
20	121
21	27
22	6
23	95
24	7
25	18
26	37
27	140
28	74
29	134
30	184

Answer 1

Arranging the data in ascending order, we get

1	6
2	6
3	7
4	9
5	16
6	18
7	27
8	29
9	31
10	37
11	37
12	54
13	58
14	58
15	64
16	74
17	79
18	81
19	89
20	95
21	96
22	108
23	121
24	130
25	134
26	140
27	184
28	206
29	222
30	249

The method by which you have found Q1 = 29, Median = 69, Q3 = 121 is the method of index

where Index of Q1 = 0.25 * 30 = 7.5, and therefore the 8th value, index of Q3 = 0.75 * 30 = 22.5, therefore the 23rd value = 121

and Q2 = 0.5 * 30 = 15, therefore the average of the 15th and the 16th value = 138/2 = 69

______________________________________________

There is another method by which we find Q1 and Q3

Where Q1 = 0.25 * (n + 1) = 0.25 * 31 = 7.75.

Therefore Q1 = 7th value + 0.75( 8th value - 7th value) = 27 + 0.75 * (29 - 27) = 27 + 1.5 = 28.5

Similarly Q3 = 0.75 * (n + 1) = 0.75 * 31 = 23.25.

Therefore Q3 = 23rd value + 0.25( 24th value - 23rd value) = 121 + 0.25 * (130 - 121) = 121 + 2.25 = 123.25