Дмитрий, доброе утро. Текст очень хороший, однако есть ошибки в грамматике, лексике, согласовании времен и употреблении предлогов. Давайте разберём их и исправим:

The data delineates the share of individuals residing alone across five distinct age cohorts at four points in time. Overall, the most striking feature of the chart is that solo living became progressively more prevalent in every age group, with the most dramatic escalation occurring among the two oldest cohorts.

Ошибка: the most striking feature… is that solo living became - смешение времен: is (Present Simple) и became (Past Simple). Поскольку речь идет о данных за длительный период, уместно использовать Present Perfect для указания на результат к настоящему моменту.

Правильный вариант: …is that solo living has become progressively more prevalent…

As regards the two younger demographics, these age categories were not taken for the report. The figure for the youngest cohort edged up marginally to around 2% by 1900, before gathering pace in the latter half of the century.

Тут две ошибки:

youngs demographies - неверная форма прилагательного и существительного. Young не имеет формы множественного числа, а правильное слово - demographics (не demographies).

Правильный вариант: the two younger demographics.

was not taken for the report - неверное согласование подлежащего и сказуемого: these age categories (множественное число) требует were.

Правильный вариант: these age categories were not taken for the report.

Standing at a mere 3% in 1850, the proportion of solo households among those aged 55-64 had more than quintupled by 2000, reaching just under 17%. The figure for the 27–36 bracket, by contrast, doubled over the final fifty years, albeit from a lower base.

Ошибка: had more than quintupled - использование Past Perfect здесь избыточно, так как нет другого прошедшего действия, относительно которого это действие предшествовало. Для указания на результат к 2000 году уместен Present Perfect.

Правильный вариант: …the proportion… has more than quintupled by 2000…

Not only did every single cohort record higher figures in 2000 than in 1950, but the gap between the youngest and oldest groups also widened considerably.

Ошибка: пропущено сравнение than in 1950 - без него фраза неполная.

Правильный вариант: …higher figures in 2000 than in 1950…

Turning to the later decades, group 27-36 has overtaken group 37-46, and this once again confirms that loneliness is becoming more common among younger people. It could be argued that the leading group from 1850 to 2000 was always the oldest group, aged 55-64.

Ошибка: group 27-36 has overtaken - если речь идет о данных, зафиксированных в прошлом (например, в 2000 году), уместнее Past Simple.

Правильный вариант: …group 27-36 overtook group 37-46…

Taken together, the figures point to a marked shift towards independent living among older Americans over the period as a whole.

В этом фрагменте ошибок нет. Предложение совершенно правильное!