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Average frequency example 2

Optional numerical practice

Extra drills; no claim that these exact questions or allocated marks appeared in TEE

Optional practice question. In a four-week campaign, 2,000 people receive 1 exposures each, 1,000 people receive 4 exposures each. The groups are distinct with no overlap. Find gross exposures, unique reach and average frequency. [3 practice marks]

Answer

Authored illustration: these numbers were chosen to explain a faculty-note concept. No matching supplied-data question was found in the 14 recovered APR papers. Standalone calculation drills are optional practice; their marks are author-set.

Given

Group	Distinct people	Exposures each
1	2000	1
2	1000	4

To find

Gross exposures, unduplicated reach and average frequency.

Formula and why

I=\sum_i n_i f_i,\qquad n=\sum_i n_i,\qquad\bar f=\frac{I}{n}

Multiply each group size by its frequency; then add. The reach sum is valid because the question explicitly says the groups do not overlap.

Step-by-step solution

Step 1. Count exposures for group 1

2000\times1=2000

Step 2. Count exposures for group 2

1000\times4=4000

Step 3. Add all group exposures

2000+4000=6000

Step 4. Count distinct people

2000+1000=3000

Step 5. Divide exposures by people reached

\bar f=\frac{6000}{3000}=2

Final answer: Gross exposures = 6,000; reach = 3,000 people; average frequency = 2.