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Mixed calculation: reach, frequency, GRP and CPM

Optional numerical practice

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

Optional practice question. A four-week campaign reaches 8,000 distinct people in a target of 20,000, generates 24,000 gross impressions and costs ₹12,000. Find reach percentage, average frequency, GRP and CPM. [5 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

TargetReachedImpressionsCost
20,0008,00024,000₹12,000

To find

Reach percentage, average frequency, gross rating points and cost per thousand impressions.

Formula and why

R_{\%}=\frac{n}{N}\times100LaTeX: R_{\%}=\frac{n}{N}\times100
\bar f=\frac{I}{n}LaTeX: \bar f=\frac{I}{n}
\text{GRP}=R_{\%}\times\bar fLaTeX: \text{GRP}=R_{\%}\times\bar f
\text{CPM}=\frac{C}{I}\times1000LaTeX: \text{CPM}=\frac{C}{I}\times1000

Here N = 20,000 target people, n = 8,000 distinct people reached, I = 24,000 impressions and C = ₹12,000 cost. The bar above f means average frequency; R with the % label means reach as a percentage number. Use the same period and target for all four measures.

Step-by-step solution

Step 1. Calculate reach

\frac{8000}{20000}\times100=40\%LaTeX: \frac{8000}{20000}\times100=40\%

Step 2. Calculate average frequency

\frac{24000}{8000}=3LaTeX: \frac{24000}{8000}=3

Step 3. Calculate GRP

40\times3=120LaTeX: 40\times3=120

Step 4. Calculate CPM

\frac{12000}{24000}\times1000=500LaTeX: \frac{12000}{24000}\times1000=500

Step 5. Check units and consistency

8,000 people × 3 exposures = 24,000 impressions, matching the given total. CPM has rupees per thousand impressions; reach has percent; frequency has exposures per reached person.

Final answer: Reach 40%; average frequency 3; 120 GRPs; CPM ₹500.