To find the average "madness per item" for the workers in the entire market, we need to follow a step-by-step process that involves summing up the "total madness" for each group and then finding the overall average.
### Step-by-Step Solution:
1. Identify the data from the table:
- For the group [tex]$250-300$[/tex]:
- Number of items = 4
- Madness per item = 8
- For the group [tex]$394-890$[/tex]:
- Number of items = 36
- Madness per item = 12
- For the group [tex]$500-8000$[/tex]:
- Number of items = 28
- Madness per item = 25
- For the group [tex]$800-1200$[/tex]:
- Number of items = 28
- Madness per item = 8.3
- For the group [tex]$120-$[/tex]:
- Number of items = 0
- Madness per item = 4
2. Calculate the total madness for each group:
- For the group [tex]$250-300$[/tex]:
[tex]\[
\text{Total Madness} = 4 \times 8 = 32
\][/tex]
- For the group [tex]$394-890$[/tex]:
[tex]\[
\text{Total Madness} = 36 \times 12 = 432
\][/tex]
- For the group [tex]$500-8000$[/tex]:
[tex]\[
\text{Total Madness} = 28 \times 25 = 700
\][/tex]
- For the group [tex]$800-1200$[/tex]:
[tex]\[
\text{Total Madness} = 28 \times 8.3 = 232.4
\][/tex]
- For the group [tex]$120-$[/tex]:
[tex]\[
\text{Total Madness} = 0 \times 4 = 0
\][/tex]
3. Sum the total madness for all groups:
[tex]\[
\text{Total Madness} = 32 + 432 + 700 + 232.4 + 0 = 1396.4
\][/tex]
4. Sum the number of items for all groups:
[tex]\[
\text{Total Count} = 4 + 36 + 28 + 28 + 0 = 96
\][/tex]
5. Calculate the average madness per item:
[tex]\[
\text{Average Madness} = \frac{\text{Total Madness}}{\text{Total Count}} = \frac{1396.4}{96} \approx 14.545833333333334
\][/tex]
### Final Result:
The average madness per item in the whole market is approximately [tex]\( 14.546 \)[/tex].
So, in summary:
- The total sum of madness is [tex]\( 1396.4 \)[/tex].
- The total count of items is [tex]\( 96 \)[/tex].
- The average madness per item for the entire market is approximately [tex]\( 14.546 \)[/tex].
