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Use dis data 4 # 1, 2, 3

Group: A: 56, 14, 26, 28, 29, 45, 32, 80, 3, 10
Group B: 27, 24, 18, 19, 5, 16, 22, 10, 6, 20

1. Find mean of A and B ( round 2 tenth ) n THEN dins their Differences

2. Find range of each student group n tell which group is more inconsistent

3. Find da median of each student group, n find their difference in medians

1 answer

Let's calculate the required values step by step.

Step 1: Find the mean of Group A and Group B

Group A:

  • Values: 56, 14, 26, 28, 29, 45, 32, 80, 3, 10
  • Mean = (Sum of values) / (Number of values)

Calculating the sum of Group A: \[ 56 + 14 + 26 + 28 + 29 + 45 + 32 + 80 + 3 + 10 = 343 \] Number of values in Group A: 10

Mean of Group A: \[ \text{Mean A} = \frac{343}{10} = 34.3 \]

Group B:

  • Values: 27, 24, 18, 19, 5, 16, 22, 10, 6, 20
  • Mean = (Sum of values) / (Number of values)

Calculating the sum of Group B: \[ 27 + 24 + 18 + 19 + 5 + 16 + 22 + 10 + 6 + 20 = 147 \] Number of values in Group B: 10

Mean of Group B: \[ \text{Mean B} = \frac{147}{10} = 14.7 \]

Difference in Means: \[ \text{Difference} = \text{Mean A} - \text{Mean B} = 34.3 - 14.7 = 19.6 \]

Step 2: Find the range of each group

Range Calculation: The range is calculated as the difference between the maximum and minimum values in each group.

Group A:

  • Max = 80
  • Min = 3 \[ \text{Range A} = 80 - 3 = 77 \]

Group B:

  • Max = 27
  • Min = 5 \[ \text{Range B} = 27 - 5 = 22 \]

Inconsistency: The group with the larger range is considered more inconsistent.

Thus, Group A (Range = 77) is more inconsistent than Group B (Range = 22).

Step 3: Find the median of each group

To find the median, we first organize the numbers in ascending order.

Group A (sorted): 3, 10, 14, 26, 28, 29, 32, 45, 56, 80

  • Median position = (10 + 1)/2 = 5.5, so we take the average of the 5th and 6th values. Median A: \[ \text{Median A} = \frac{28 + 29}{2} = \frac{57}{2} = 28.5 \]

Group B (sorted): 5, 6, 10, 16, 18, 19, 20, 22, 24, 27

  • Median position = (10 + 1)/2 = 5.5, so we take the average of the 5th and 6th values. Median B: \[ \text{Median B} = \frac{18 + 19}{2} = \frac{37}{2} = 18.5 \]

Difference in Medians: \[ \text{Difference} = \text{Median A} - \text{Median B} = 28.5 - 18.5 = 10 \]

Summary of Results

  1. Mean of Group A: 34.3, Mean of Group B: 14.7, Difference: 19.6
  2. Range of Group A: 77, Range of Group B: 22, Group A is more inconsistent.
  3. Median of Group A: 28.5, Median of Group B: 18.5, Difference in Medians: 10.