From the data 4, 5, 5, 2, 3, 1, 6, which statements are true?
- Median =4.
- Range =6.
- Range − median =1.
- Mean =4.5.
Explanation
Sort the data from smallest to largest:
1,2,3,4,5,5,6
Number of data points n=7.
Statement 1 Analysis
The median is the 2n+1=28=4-th value. The 4-th value is 4.
Me=4
Statement 1 is CORRECT.
Statement 2 Analysis
The range is the difference between the maximum and minimum values.
Range=xmax−xmin=6−1=5
Statement 2 is INCORRECT (should be 5, not 6).
Statement 3 Analysis
Difference between range and median:
Range−Me=5−4=1
Statement 3 is CORRECT.
Statement 4 Analysis
The mean (xˉ) is the sum of all data divided by the number of data points.
xˉ=71+2+3+4+5+5+6=726=375
The value 375 is not equal to 4.5. Statement 4 is INCORRECT.
Conclusion
The correct statements are (1) and (3).