A company conducted a consumer survey and collected data on annual income ranges for its customers. The data is summarized in the following table (in USD):
| Income Range |
Frequency |
| 20000-30000 |
5 |
| 30000-40000 |
12 |
| 40000-50000 |
20 |
| 50000-60000 |
8 |
| 60000-70000 |
5 |
Using this data:
(a) Summarize the data by calculating the mean, median, and interquartile range (IQR).
(b) Based on your statistical findings, propose a marketing decision to target the most relevant consumer segment.
Question
Summarize the consumer survey data by computing the mean, median, and interquartile range (IQR). Use the provided frequency table of income ranges:
| Income Range |
Frequency |
| 20000-30000 |
5 |
| 30000-40000 |
12 |
| 40000-50000 |
20 |
| 50000-60000 |
8 |
| 60000-70000 |
5 |
Show all calculations for grouped data measures.
Hint
Hint
Hint
Remember to use class midpoints for the mean and cumulative frequencies for median and quartile identification.
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Answer
Answer
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Explanation
Explanation
- Formula Booklet
Complete Answer
Mean: approximately 44200, Median: approximately 44000, IQR: approximately 14375
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Answer Explanation
Answer Explanation
Question
Based on the statistical summary from part (a), propose a marketing decision to effectively target the consumer segment represented in the survey data. Justify your decision using the computed measures.
Hint
Hint
Hint
Consider how the similarity between the mean and median indicates a symmetric distribution and what a moderate IQR implies about income variability.
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Answer
Answer
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Explanation
Explanation
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Complete Answer
Given the mean income of approximately $44,200 and a median income of approximately $44,000, the income distribution is roughly symmetric, suggesting a central income group. The IQR of approximately $14,375 indicates a moderate spread of income. A marketing strategy focusing on products or services priced in the mid-range, appealing to the average income group, would be most effective. This could involve highlighting value for money and targeting marketing efforts towards channels frequented by a broad income demographic.
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Mark Scheme
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Answer Explanation
Answer Explanation
