Toothpaste Market Research Survey Analysis

Question 1

What is the average price of a toothpaste used by a household with income of over Rs. 5,000?

Accepted Answer

D. Since the price interval `> 10` is open-ended, the exact midpoint for this highest category cannot be specified without upper-bound information. Consequently, the precise mean price cannot be determined.

Question 2

What is the probability of a household with income less than or equal to Rs. 5,000 p.m. using a toothpaste costing less than Rs. 8?

Accepted Answer

B. Total households with income $\le 5,000$: Col 1 ($< 1500$) = $1500 + 1750 + 500 + 250 + 50 = 4050$ Col 2 ($1500	ext{--}2500$) = $500 + 750 + 1200 + 450 + 100 = 3000$ Col 3 ($2500	ext{--}3500$) = $350 + 400 + 500 + 250 = 1500$ Col 4 ($3500	ext{--}5000$) = $150 + 200 + 400 + 300 = 1050$ Total = $4050 + 3000 + 1500 + 1050 = 9600$. Households among these using toothpaste $< 8$ (rows $<4$, $4	ext{--}6$, $6	ext{--}8$): Row $< 4$: $1500 + 500 = 2000$ Row $4	ext{--}6$: $1750 + 750 + 350 + 150 = 3000$ Row $6	ext{--}8$: $500 + 1200 + 400 + 200 = 2300$ Total = $2000 + 3000 + 2300 = 7300$. Probability = $\frac{7300}{9600} \approx 0.7604 \approx 0.76$.

Question 3

If a family uses a toothpaste priced at between Rs. 6 and Rs. 8, what is the probability that its income is at least Rs. 2,500 p.m.?

Accepted Answer

C. Consider the row for price between Rs. 6 and Rs. 8: Total households in this row = $500 + 1200 + 400 + 200 + 50 = 2350$. Households in this row with income $\ge 2,500$ (columns $2500	ext{--}3500$, $3500	ext{--}5000$, $>5000$): $400 + 200 + 50 = 650$. Probability = $\frac{650}{2350} \approx 0.2766 \approx 0.28$.

Question 4

What is the ratio of households with income of less than Rs. 1,500 p.m. to the total number of households?

Accepted Answer

C. Total households in column $< 1500$ = $1500 + 1750 + 500 + 250 + 50 = 4050$. Sum of all entries across all columns: Col 1 = 4050 Col 2 = 3000 Col 3 = 1500 Col 4 = 1050 Col 5 ($>5000$) = $0 + 50 + 50 + 100 + 200 = 400$ Total households = $4050 + 3000 + 1500 + 1050 + 400 = 10000$. Ratio = $\frac{4050}{10000} = 0.405$.

Question 5

Which of the following can be definitely stated? I. As income increases, consumption of low-priced toothpastes drops. II. Lower the income, no expensive toothpaste will be used by that household. III. More than 50% of the households have incomes less than Rs. 2,500 p.m.

Accepted Answer

C. Let's evaluate each statement: - **Statement I**: For low-priced toothpastes ($< 4$ and $4	ext{--}6$), household counts decrease steadily as income increases. True. - **Statement II**: For income $< 1500$, there are still 50 households using $>10$ priced toothpastes, so this statement is false. - **Statement III**: Households with income $< 2500$ = $4050 + 3000 = 7050$, which is $70.5\%$ of $10000$, well over $50\%$. True. Thus, statements I and III are definitely true.

Toothpaste Market Research Survey Analysis

Passage / data set

Question 1 of 5

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Question 2 of 5

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Question 3 of 5

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Question 4 of 5

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Question 5 of 5

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Practise this under exam conditions

Price of toothpaste used (Rs.)	< Rs. 1,500	Rs. 1,500-2,500	Rs. 2,500-3,500	Rs. 3,500-5,000	> Rs. 5,000
< 4	1500	500	—	—	—
4 – 6	1750	750	350	150	50
6 – 8	500	1200	400	200	50
8 – 10	250	450	500	400	100
> 10	50	100	250	300	200