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Average frequency example 1

Optional numerical practice

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

Faculty-note worked example. In a four-week campaign, 1,500 people receive 3 exposures each, 1,500 people receive 6 exposures each. The groups are distinct with no overlap. Find gross exposures, unique reach and average frequency. [3 practice marks]

Answer

Faculty-note worked example: the values come from APR M2 notes p27. The question has been rewritten to teach the steps; this is not verbatim PYQ wording. Any practice-mark allocation is author-set.

Given

Group	Distinct people	Exposures each
1	1500	3
2	1500	6

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

1500\times3=4500

Step 2. Count exposures for group 2

1500\times6=9000

Step 3. Add all group exposures

4500+9000=13500

Step 4. Count distinct people

1500+1500=3000

Step 5. Divide exposures by people reached

\bar f=\frac{13500}{3000}=4.5

Final answer: Gross exposures = 13,500; reach = 3,000 people; average frequency = 4.5.