# Average frequency example 2

Subject: Advertising and Public Relations

Exam: TEE

Reader: https://deep-learning-study-room.vercel.app/apr/#tee/practice/numbers/frequency2

Canonical: https://deep-learning-study-room.vercel.app/read/apr/tee/practice/numbers--frequency2/

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.

#### Practical interpretation · What the answer means

2 is the average number of opportunities among reached people. It does not mean each individual had exactly that many exposures.