A researcher is presenting the results of a randomised trial investigating the use of a fungal infection in the reduction of a weed. Plants infected with the fungus were compared with control plants. Plants were in pots, and after a two-month growth period, the weeds in each pot were cut and the fresh weight of the weeds in grams was recorded.

The researcher provides the following summary statistics:

Treatment

Number

Mean

Standard deviation

Fungal

20

19.4

6.5

Control

20

23.4

7.2

She also presents some graphs of the data. Assuming the summary statistics are correct, which one is the correct graph of the data from the set below?

Question

A researcher is presenting the results of a randomised trial investigating the use of a fungal infection in the reduction of a weed.  Plants infected with the fungus were compared with control plants.  Plants were in pots, and after a two-month growth period, the weeds in each pot were cut and the fresh weight of the weeds in grams was recorded.

The researcher provides the following summary statistics:

Treatment

Number

Mean

Standard deviation

Fungal

20

19.4

6.5

Control

20

23.4

7.2

She also presents some graphs of the data.  Assuming the summary statistics are correct, which one is the correct graph of the data from the set below?

BlackTom AI · Accepted Answer

To evaluate which graph is correct, we start from the given summary statistics for the two groups. The fungal treatment has n = 20, mean = 19.4, and SD = 6.5. The control treatment has n = 20, mean = 23.4, and SD = 7.2. This means the fungal group’s average weed weight is 4.0 units lower than the control group, and both groups have similar variability, with standard deviations around 6.5–7.2 and equal sample sizes.

Option A: If this graph showed the fungal group centered around 19.4 and the control group centered around 23.4 but with markedly different spreads (for example, one group with a very small spread and the other with a very large spread), it would be inconsistent with the reported SDs of 6.5 and 7.2. Additionally, if the means were reversed or the means were not separated by roughly 4 units, that would be incorrect. In short, A would be wrong if any of these misalignments occurred.

Option B: If B placed the fungal group’s mean higher than the control group, or if the separation between the group means did not approximate 4 units, it would misstate the direction or magnitude of the difference. Since the correct data show the fungal group lower (19.4) than the control (23.4), any graph displaying the opposite relationship or a visibly incorrect difference is incorrect.

Option C: This option correctly reflects the given numbers if it shows the fungal group centered at about 19.4 with a spread around 6.5, and the control group centered at about 23.4 with a spread around 7.2, with the two distributions overlapping substantially due to the relatively large standard deviations. The mean difference appears as roughly 4 units in the negative direction (fungal < control), and the sample sizes being equal helps ensure the visual comparison is balanced. If C matches these relationships, it is consistent with the supplied statistics.

Option D: If D depicted either group with the wrong mean values, the wrong direction of difference, or a non-symmetric or exaggerated spread inconsistent with 6.5 and 7.2, then it would be incorrect. Also, any portrayal that implies markedly less overlap between the distributions than is suggested by the relatively large SDs would misrepresent the data given the numbers.

In summary, the correct graph must place the fungal treatment mean at 19.4 and the control mean at 23.4, with similar spreads (SDs 6.5 and 7.2) and equal sample sizes (20 per group), leading to a mean difference of -4.0 and noticeable overlap between distributions. The other options would be incorrect if they violate any of these conditions: wrong mean values, wrong direction of difference, inconsistent SDs, or unequal sample sizes. The provided correct choice is the one that aligns with all these facts, namely option C.

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