Answer:
The interquartile range of the new set is less than the interquartile range of the original set.
Step-by-step explanation:
Given : 69, 70, 72, 72, 74, 74, 74, 75, 76, 76, 76, 77, 77, 82
To Find : If the highest and lowest numbers were dropped to form a new set of data how would the inter quartile range of the new set compare to the inter quartile range of the original set?
Solution:
Data : 69, 70, 72, 72, 74, 74, 74, 75, 76, 76, 76, 77, 77, 82
No. of terms = 14
Median =
Median =
Median =
Median =
Median =
is the median of the lower half of data ( data below the median)
Data : 69, 70, 72, 72, 74, 74, 74
No. of terms = 7
Median = 4th term =72
is the median of the upper half of data ( data above the median)
Data : 75, 76, 76, 76, 77, 77, 82
No. of terms = 7
Median = 4th term =76
IQR =
<u>Now the highest and lowest numbers were dropped to form a new set of data</u>
So, new data : 70, 72, 72, 74, 74, 74, 75, 76, 76, 76, 77, 77
No. of terms = 12
Median =
Median =
Median =
Median =
Median =
is the median of the lower half of data ( data below the median)
Data: 70, 72, 72, 74, 74, 74,
No. of terms = 6
Median =
Median =
is the median of the upper half of data ( data above the median)
Data : 75, 76, 76, 76, 77, 77
No. of terms = 6
Median =
Median =
IQR =
Thus IQR of old data set is greater than IQR of new data set i.e. 4>3
Hence The interquartile range of the new set is less than the interquartile range of the original set.