1. Mean of Group A and Group B
Group A: The numbers are: 56, 14, 26, 28, 29, 45, 32, 80, 3, 10.
To find the mean: \[ \text{Mean A} = \frac{\text{Sum of Group A}}{\text{Count of Group A}} = \frac{56 + 14 + 26 + 28 + 29 + 45 + 32 + 80 + 3 + 10}{10} = \frac{ 56 + 14 + 26 + 28 + 29 + 45 + 32 + 80 + 3 + 10 }{ 10 } = \frac{ 302 }{ 10 } = 30.2 \]
Group B: The numbers are: 27, 24, 18, 19, 5, 16, 22, 10, 6, 20.
To find the mean: \[ \text{Mean B} = \frac{\text{Sum of Group B}}{\text{Count of Group B}} = \frac{27 + 24 + 18 + 19 + 5 + 16 + 22 + 10 + 6 + 20}{10} = \frac{ 27 + 24 + 18 + 19 + 5 + 16 + 22 + 10 + 6 + 20 }{ 10 } = \frac{ 147 }{ 10 } = 14.7 \]
Difference in Means: \[ \text{Difference} = \text{Mean A} - \text{Mean B} = 30.2 - 14.7 = 15.5 \]
2. Range of Each Student Group
Group A: Max = 80, Min = 3 \[ \text{Range A} = \text{Max} - \text{Min} = 80 - 3 = 77 \]
Group B: Max = 27, Min = 5 \[ \text{Range B} = \text{Max} - \text{Min} = 27 - 5 = 22 \]
Inconsistency Comparison: Group A has a larger range (77), indicating it is more inconsistent compared to Group B (22).
3. Median of Each Student Group
Group A: Sorted: 3, 10, 14, 26, 28, 29, 32, 45, 56, 80. Since there is an even number of values (10), the median is the average of the 5th and 6th values. Median A = (28 + 29) / 2 = 28.5
Group B: Sorted: 5, 6, 10, 16, 18, 19, 20, 22, 24, 27. Median B = (18 + 19) / 2 = 18.5
Difference in Medians: \[ \text{Difference in Medians} = \text{Median A} - \text{Median B} = 28.5 - 18.5 = 10.0 \]
4. Surveying Every 5th Woman Using the Copier
No, surveying every 5th woman who uses the copier is not a random, representative sample. This is because the sample is biased toward women who use the copier, which may not be representative of all women in the company. It may exclude women who do not use the copier or only those who happen to use it at certain times, leading to skewed results.
5. Estimate of Students Owning Cats
Using the proportion of students who own cats: \[ \text{Fraction of Students Owning Cats} = \frac{4}{50} \]
To estimate the total number of students owning cats among 800 students: \[ \text{Estimated Number of Cat Owners} = \frac{4}{50} \times 800 = 64 \]
Therefore, it is estimated that 64 students own cats.