The figures relate to eight key diagnostic tests: upper endoscopy, lower endoscopy, colonoscopy, cystoscopy, CT scan, MRI scan, barium studies and non-obstetric ultrasound.
As of the end of September, 102,716 patients were waiting to be seen for these tests.
This is 15,292 more people than on the same date in 2019, an increase of 17.5 per cent.
Of those, 47 per cent had been waiting for longer than six weeks, compared to 18 per cent in 2019.
Almost 70,000 patients were waiting for a radiology test, 4.9 per cent higher than in September 2019.
Some 16 percent of those waiting for a radiology test had been waiting longer than 13 weeks, while 179 people had been waiting for over a year.
The greatest reduction in the number of patients who had been waiting over six weeks was reported for MRI scans, dropping from 11,766 at June 30 2020 to 3,541.
In addition to increased local capacity in some health board areas, this decrease is partly due to six MRI vans being rotated around Scotland, targeting areas of higher demand.
The waiting time standard for one of the eight key diagnostic tests and investigations is no longer than six weeks.
This is a component of the NHS Scotland goal to deliver 90 per cent of patients from referral to treatment in 18 weeks.
As of September 30, 67 per cent of patients were being treated within that time frame across Scotland, compared to 79 per cent in the same quarter of 2019.
This year’s figures exclude NHS Borders, Grampian and Lothian, who were not able to provide data for the third quarter because of the Covid-19 pandemic.
The figures for July and August were 70 per cent and 66 percent.
Public Health Scotland noted an overall downward trend in performance due to an increasing number of patients whose wait was paused during lockdown now being treated each month.
Delivery of a patient from referral to treatment is dependent on waiting times for diagnostic tests, outpatient appointments, inpatient and day case treatment.
Non-urgent elective services were paused in March due to Covid-19, and began to resume from June 19.