# Mixed calculation: reach, frequency, GRP and CPM

Subject: Advertising and Public Relations

Exam: TEE

Reader: https://deep-learning-study-room.vercel.app/apr/#tee/practice/numbers/combined

Canonical: https://deep-learning-study-room.vercel.app/read/apr/tee/practice/numbers--combined/

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

| Target | Reached | Impressions | Cost |
| --- | --- | --- | --- |
| 20,000 | 8,000 | 24,000 | ₹12,000 |

## To find

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

## Formula and why



$$
R_{\%}=\frac{n}{N}\times100
$$





$$
\bar f=\frac{I}{n}
$$





$$
\text{GRP}=R_{\%}\times\bar f
$$





$$
\text{CPM}=\frac{C}{I}\times1000
$$



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



$$
\frac{8000}{20000}\times100=40\%
$$



#### Step 2. Calculate average frequency



$$
\frac{24000}{8000}=3
$$



#### Step 3. Calculate GRP



$$
40\times3=120
$$



#### Step 4. Calculate CPM



$$
\frac{12000}{24000}\times1000=500
$$



#### 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.

#### Practical interpretation · What the answer means

The campaign reached fewer than half the target, with three average opportunities among those reached. Whether it succeeded depends on its objective, audience fit and message effect.