Answer:
The Interquartile range is 188
Step-by-step explanation:
Missing Data:
1,19,35,43,49,55,63,94,105,110,175,231,239,351,738
Required
Determine the Interquartile range (IQR)
The given data is ordered already.
First, we need to determine the median
For odd number of data
Median = ½(n + 1)th
In this case, n = 15; so
Median = ½(15 + 1)th
Median = ½(16)th
Median = 8th
This implies that the median is at the 8th position.
So, we have:
1,19,35,43,49,55,63 ----> Lower
(94) ---- Median
105,110,175,231,239,351,738 ---- Upper
Next, we determine the median of the lower and upper sets.
These are called lower quartile (Q1) and upper quartile (Q3) respectively
Lower: 1,19,35,43,49,55,63
Number of data, n = 7
Q1 = ½(n + 1)th
Q1 = ½(7 + 1)th
Q1 = ½(8)th
Q1 = 4th position
From the list of data in the lower set,
Q1 = 43
Upper: 105,110,175,231,239,351,738
Number of data, n = 7
Q3 = ½(n + 1)th
Q3 = ½(7 + 1)th
Q3 = ½(8)th
Q3 = 4th position
From the list of data in the upper set,
Q3 = 231
IQR is then calculated as thus:
IQR = Q3 - Q1
IQR = 231 - 43
IQR = 188
