Question
In: Statistics and Probability
A sample of 9 residents’ incomes in a particular town yields the following descriptive statistics: $19,000...
A sample of 9 residents’ incomes in a particular town yields the following descriptive statistics:
| $19,000 | $20,000 | $27,000 |
| $38,000 | $112,000 | $45,000 |
| $22,000 | $49,000 | $32,000 |
What is the interquartile range for this
sample?
Solutions
Expert Solution
Interquartile range is the difference between 3rd quartile and 1st quartile, which means if we have to find the Interquartile range we need to find the 1st and 3rd quartile.
To find the 1st and 3rd quartile, first we need to arrange the data in ascending order.
1st quartile is value which corresponds to n/4 th observation when the data is arranged in ascending order.
here we have n=9, so n/4=9/4 = 2.25 ≈ 3
so the 1st quartile is 3rd observation when arranged in ascending order.
3rd quartile is value which corresponds to 3n/4 th observation when the data is arranged in ascending order.
here we have n=9, so 3n/4=3*9/4 = 6.75 ≈ 7
so the 3rd quartile is 7th observation when arranged in ascending order.
| SN | x | Quartile |
| 1 | 19000 | |
| 2 | 20000 | |
| 3 | 22000 | Q1 |
| 4 | 27000 | |
| 5 | 32000 | Median |
| 6 | 38000 | |
| 7 | 45000 | Q3 |
| 8 | 49000 | |
| 9 | 112000 |
Hence Q1= 22000 and Q3= 45000
So , the interquartile range can be obtained as below:
IQR= Q3 -Q1
IQR = 45000 - 22000
IQR = 23000
Hence the interquartile range for this sample is 23000.
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