Kerri is growing ten plants for a science project. She measures their growth after one month. Her data is shown in the table.

Question

 
  Plant A Plant B Plant C Plant D Plant E Plant F  Plant G Plant H Plant I
Plant J
,begin bold,Growth,end bold,
(centimeters)
4
4
6
7
7
8
8
9
9
18

Question 1
,begin emphasis,Part A,end emphasis,
Which measure of center ,begin emphasis,most,end emphasis, accurately describes the growth of the plants over the month?

Answer 1

To determine which measure of center most accurately describes the growth of the plants, we need to consider the three main measures of center: mean, median, and mode.

First, let's look at the growth data:

• Plant A: 4 cm
• Plant B: 4 cm
• Plant C: 6 cm
• Plant D: 7 cm
• Plant E: 7 cm
• Plant F: 8 cm
• Plant G: 8 cm
• Plant H: 9 cm
• Plant I: 9 cm
• Plant J: 18 cm

Now we'll calculate each measure of center:

1. Mean: \[ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} = \frac{4 + 4 + 6 + 7 + 7 + 8 + 8 + 9 + 9 + 18}{10} = \frac{80}{10} = 8 \]

2. Median: To find the median, we need to sort the data: 4, 4, 6, 7, 7, 8, 8, 9, 9, 18 The median is the average of the 5th and 6th values (since there are 10 values): \[ \text{Median} = \frac{7 + 8}{2} = 7.5 \]

3. Mode: The mode is the value that appears most frequently. In this case, both 4 and 7 appear twice, so the modes are 4 and 7.

Conclusion:

• The mean (8) is influenced heavily by the outlier (18) and may not accurately represent the central tendency of the majority of the plants.
• The median (7.5) is more representative of the middle of the data.
• The mode (4 and 7) indicates the most common values but does not reflect the entire dataset effectively due to the presence of the outlier.

Given the presence of the outlier (18), the median most accurately describes the growth of the plants over the month, as it is not skewed by the extreme value.