Let's calculate the statistics step-by-step for both Student Group A and Student Group B.
Step 1: Calculate the Mean
Group A:
Values: 56, 14, 26, 28, 29, 45, 32, 80, 3, 10
Mean of Group A = (Sum of values) / (Number of values)
= (56 + 14 + 26 + 28 + 29 + 45 + 32 + 80 + 3 + 10) / 10
= 323 / 10
= 32.3 (rounded to tenth)
Group B:
Values: 27, 24, 18, 19, 5, 16, 22, 10, 6, 20
Mean of Group B = (Sum of values) / (Number of values)
= (27 + 24 + 18 + 19 + 5 + 16 + 22 + 10 + 6 + 20) / 10
= 147 / 10
= 14.7 (rounded to tenth)
Difference in Means:
Mean A - Mean B = 32.3 - 14.7 = 17.6
Step 2: Calculate the Range
Range of Group A:
Range = Maximum - Minimum
= 80 - 3 = 77
Range of Group B:
Range = Maximum - Minimum
= 27 - 5 = 22
Group A has a range of 77 and Group B has a range of 22. Therefore, Group A is more inconsistent since it has a larger range.
Step 3: Calculate the Median
Median of Group A:
First, sort the values: 3, 10, 14, 26, 28, 29, 32, 45, 56, 80
Since there are 10 values (even), the median is the average of the 5th and 6th values.
Median = (28 + 29) / 2 = 57 / 2 = 28.5
Median of Group B:
First, sort the values: 5, 6, 10, 16, 18, 19, 20, 22, 24, 27
Since there are 10 values (even), the median is the average of the 5th and 6th values.
Median = (18 + 19) / 2 = 37 / 2 = 18.5
Difference in Medians:
Median A - Median B = 28.5 - 18.5 = 10.0
Summary of Results
- Mean of Group A: 32.3
- Mean of Group B: 14.7
- Difference in Means: 17.6
- Range of Group A: 77
- Range of Group B: 22
- Group A is more inconsistent.
- Median of Group A: 28.5
- Median of Group B: 18.5
- Difference in Medians: 10.0