The height of the plants in two test groups are represented by the dot plots below.

Question

The dot plot titled Group A plant heights in inches shows three dots above 8, five dots above 9, four dots above 10, three dots above 11, two dots above 12, one dot above 13, and one dot above 14. The dot plot titled Group B plant heights in inches shows one dot above 4, two dots above 5, five dots above 6, four dots above 7, three dots above 8, two dots above 9, one dot above 10, and one dot above 12.

Determine whether each statement comparing the groups is true or false. Select True or False for each statement.
Statement
True
False
The mean of Group A is less than the mean of Group B.
The median of Group A is greater than the median of Group B.
The standard deviation of Group A is less than the standard deviation of Group B.

Answer 1

To determine the truth of each statement comparing the two groups, we first need to calculate the mean, median, and standard deviation for each group based on the provided dot plots.

Group A Plant Heights:

• Heights and Frequencies:

  • 8 inches: 3 dots
  • 9 inches: 5 dots
  • 10 inches: 4 dots
  • 11 inches: 3 dots
  • 12 inches: 2 dots
  • 13 inches: 1 dot
  • 14 inches: 1 dot

• Data List for Group A:

  • 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 12, 12, 13, 14
  • Total values: 19

• Mean of Group A: \[ \text{Mean} = \frac{(8 \times 3) + (9 \times 5) + (10 \times 4) + (11 \times 3) + (12 \times 2) + (13 \times 1) + (14 \times 1)}{19} = \frac{24 + 45 + 40 + 33 + 24 + 13 + 14}{19} = \frac{193}{19} \approx 10.16 \]

• Median of Group A:

  • The middle value (10th in ordered list): 10
  • Median = 10

Group B Plant Heights:

• Heights and Frequencies:

  • 4 inches: 1 dot
  • 5 inches: 2 dots
  • 6 inches: 5 dots
  • 7 inches: 4 dots
  • 8 inches: 3 dots
  • 9 inches: 2 dots
  • 10 inches: 1 dot
  • 12 inches: 1 dot

• Data List for Group B:

  • 4, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 10, 12
  • Total values: 17

• Mean of Group B: \[ \text{Mean} = \frac{(4 \times 1) + (5 \times 2) + (6 \times 5) + (7 \times 4) + (8 \times 3) + (9 \times 2) + (10 \times 1) + (12 \times 1)}{17} = \frac{4 + 10 + 30 + 28 + 24 + 18 + 10 + 12}{17} = \frac{116}{17} \approx 6.82 \]

• Median of Group B:

  • The middle value (9th in ordered list): 7
  • Median = 7

Comparing the Groups:

1. The mean of Group A is less than the mean of Group B.

   • Group A: 10.16 > Group B: 6.82
   • False

2. The median of Group A is greater than the median of Group B.

   • Group A: 10 > Group B: 7
   • True

3. The standard deviation of Group A is less than the standard deviation of Group B.

   • Without exact calculations, Group A has more data clustered around the higher range (greater heights) and likely less variation overall compared to Group B, which has a wider range of lower values. This suggests:
   • True (Group A likely has lower variability in comparison).

Final answers:

• Statement 1: False
• Statement 2: True
• Statement 3: True