Errors:  

- illustrates" is more commonly used for diagrams, "shows" might be better.

- the vaccination impact" should be "the impact of vaccination".

- reported cases of whooping cough" can be simplified.

Corrected version:

The graph shows the impact of vaccination on the cases of whooping cough in Britain (1940-1990).

Improved version:

The graph demonstrates the effect of vaccination on the incidence of whooping cough in Britain from 1940 to 1990.

Errors:  

- Through the bar graph" is unnecessary as the graph type is already mentioned.

- indirectly proportional" might be misunderstood, "inverse relationship" is clearer.

Corrected version:

We can see that the vaccination dosage is inversely related to the cases of illness.

Improved version:

The graph reveals an inverse relationship between vaccination dosage and the incidence of whooping cough.

Errors:  

- reached at a peak" should be "reached a peak".

- Missing comma after "170000".

Corrected version:

In 1940, there was a sudden increase in the number of patients suffering from whooping cough, reaching a peak of 170,000.

Improved version:

In 1940, the number of whooping cough patients surged, reaching a peak of 170,000.

Errors:  

- Missing comma after "60000".

- during 1945" should be "by 1945.

Corrected version:

However, the number of cases plunged dramatically, hitting a low of 60,000 by 1945.

Improved version:

However, by 1945, the number of cases had plunged dramatically to a low of 60,000.

Errors: 

- Incomplete phrase "After the.

- wildely" should be "wildly.

- this time" is redundant.

Corrected version:

After this, the number of cases went up and down wildly but the trend was upward.

Improved version:

Following this period, the number of cases fluctuated wildly, but the overall trend was upward.

Errors: 

- eratically" should be "erratically.

- begin" should be "began".

- Sentence structure is awkward and confusing.

Corrected version:

After a short period of time, the reported cases decreased erratically and by mid-1955, when the cases began to rise again, that was the time when the vaccination process started.

Improved version:

Shortly after, the reported cases decreased erratically until mid-1955, when they began to rise again, marking the start of the vaccination process.

Errors: 

- starts" should be "started.

- fluctuantly" should be "fluctuantly" (not a word), "fluctuating" is correct.

Corrected version:

With the introduction of the vaccine, the number of reported cases started decreasing fluctuating.

Improved version:

With the introduction of the vaccine, the number of reported cases began to decrease, albeit with fluctuations.

Errors: 

- percentage of vaccine uptake" should be "vaccine uptake percentage".

- decreased to a low of 30" is unclear, should specify percentage.

- due to which" is awkward, "causing" is better.

Corrected version:

In 1975, the vaccine uptake percentage decreased to a low of 30%, causing the number of patients to spike.

Improved version:

In 1975, the vaccine uptake percentage fell to a low of 30%, causing a spike in the number of patients.

Errors: 

- dosage proportion" is unclear, "vaccination dosage" is better.

Corrected version:

In order to control the rising cases, the vaccination dosage was increased.

Improved version:

To control the rising cases, the vaccination dosage was increased.

Errors: 

- fall" should be "fell.

- during the 20s" is unclear, should specify the decade.

- almost at zero" should be "to almost zero.

Corrected version:

The number of cases fell again gradually and during the 1970s, the figures for the reported cases went down to almost zero.

Improved version:

The number of cases gradually fell again, and by the 1970s, the reported cases had dropped to nearly zero.

Errors: 

- Through the given data" is redundant.

- the wise step which was taken" should be "a wise step.

Corrected version:

We can say that the vaccination was a wise step taken to reduce the number of whooping cough cases in Britain.

Improved version:

The data suggests that vaccination was a prudent measure to reduce the incidence of whooping cough in Britain.

Errors: 

- the essential part" should be "an essential part.

Corrected version:

However, the selection of the dosage quantity is also an essential part of the process.

Improved version:

However, determining the appropriate dosage is also a crucial part of the vaccination process.