A market research survey conducted by Company-Check was looking at the reason why
small businesses fail. From a group of 84 businesses that failed they discovered the
following: 41 failed because of a lack of funds; 36 failed because of a lack of marketing
skills; and 30 failed because of a lack of financial control; 16 of them failed because of a lack
of marketing skills and financial control; 6 failed because of a lack of funds and marketing
skills; Seventeen failed because of lack of marketing skills only; 8 because of a lack of
financial control only; and 5 failed because of other reasons.
(a) Draw a Venn diagram to illustrate this information.
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To draw a Venn diagram to illustrate this information, we first need to determine the overlapping relationships between the different factors (lack of funds, lack of marketing skills, and lack of financial control) that contributed to the failure of the small businesses.
Based on the given information, we can identify the following:
- 41 businesses failed due to a lack of funds.
- 36 businesses failed due to a lack of marketing skills.
- 30 businesses failed due to a lack of financial control.
- 16 businesses failed due to a lack of marketing skills and financial control.
- 6 businesses failed due to a lack of funds and marketing skills.
- 17 businesses failed due to a lack of marketing skills only.
- 8 businesses failed due to a lack of financial control only.
- 5 businesses failed due to other reasons (not specified).
Now, let's create a Venn diagram to represent this information.
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|____________|
| _______|
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|_____|_____|
We will label the three intersecting sections of the Venn diagram as follows:
- The left section represents businesses that failed due to a lack of funds.
- The right section represents businesses that failed due to a lack of marketing skills.
- The middle section represents businesses that failed due to a lack of financial control.
Now, let's place the numbers we have in the appropriate sections of the Venn diagram:
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| 6 |
|____________|
| 11 |
| | |
|_____|_____|
From the given information, we know that 16 businesses failed due to a lack of marketing skills and financial control. Since we have already accounted for 6 businesses that failed due to both a lack of funds and marketing skills, we subtract 6 from 16 to get 10 businesses that failed due to a lack of marketing skills and financial control only. We place this number in the overlapping section.
Next, we add the remaining number of businesses that failed due to a lack of marketing skills only (17) and place it in the right section. Similarly, we add the remaining number of businesses that failed due to a lack of financial control only (8) and place it in the left section.
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| 6 |
|____________|
| 10 |
| | |
|_____|_____|
Finally, we have 41 businesses that failed due to a lack of funds. Since we have already accounted for 6 businesses that failed due to both a lack of funds and marketing skills, and 10 businesses that failed due to both a lack of funds and financial control, we subtract these numbers from 41 to get 25 businesses that failed due to a lack of funds only. We place this number in the left section.
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| 6 |
|____________|
| 10 |
| 25 | |
|_____|_____|
This completes the Venn diagram, which accurately represents the given information about the reasons for small business failure.