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Average frequency example 3

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, 6,000 people receive 5 exposures each, 6,000 people receive 7 exposures each, 3,000 people receive 3 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 p28. 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	6000	5
2	6000	7
3	3000	3

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

6000\times5=30000

Step 2. Count exposures for group 2

6000\times7=42000

Step 3. Count exposures for group 3

3000\times3=9000

Step 4. Add all group exposures

30000+42000+9000=81000

Step 5. Count distinct people

6000+6000+3000=15000

Step 6. Divide exposures by people reached

\bar f=\frac{81000}{15000}=5.4

Final answer: Gross exposures = 81,000; reach = 15,000 people; average frequency = 5.4.