c c height 2 3 4 5 6 frequency 2 4 5 3 1 The table shows the distribution of the height of plants in a…

Analyze the question: We need the mean of a frequency distribution. Each height is weighted by how many plants have that height.

Concept: Mean = Σfx ÷ Σf

Solution:

| Height (x) | Frequency (f) | fx | |---|---|---| | 2 | 2 | 4 | | 3 | 4 | 12 | | 4 | 5 | 20 | | 5 | 3 | 15 | | 6 | 1 | 6 |

• Σf = 2 + 4 + 5 + 3 + 1 = 15
• Σfx = 4 + 12 + 20 + 15 + 6 = 57

Mean = 57 ÷ 15 = 3.8

Answer: The mean height is 3.8, which is option A.

Tip: Always build an fx column and add it up carefully. A quick check is that the mean must lie between the smallest and largest values (2 and 6). Since most of the frequency sits around 3 and 4, an answer near 3.8 is sensible.