Question

Statistics

Posted 4 months ago

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Matheus ordered hydrangeas (a kind of flower) to decorate for a wedding. The stem plot gives the diameters, in inches, of the 35 heads of the hydrangeas that arrived.
Key: $7 \mid 7=7.7$ inches
Which of the following is the closest estimate to the percentile for the hydrangea head with a 5.2 inch diameter?
Choose 1 answer:
(A) $37^{\text {th }}$ percentile
(B) $41^{\text {st }}$ percentile
(c) $48^{\text {th }}$ percentile
(D) $55^{\text {th }}$ percentile
```

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Answer from Sia

Posted 4 months ago

Solution by Steps

step 1

Identify the position of the hydrangea head with a 5.2 inch diameter in the stem and leaf plot. The stem 5 has leaves: 0, 1, 1, 2, 3, 3, 3, 3, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8. The 5.2 inch diameter corresponds to the leaf 2

step 2

Count the number of data points less than 5.2 inches. The leaves less than 2 in stem 5 are: 0, 1, 1. Additionally, all leaves in stems 3 and 4 are less than 5.2 inches. Thus, the total count is 1 (stem 3) + 9 (stem 4) + 3 (stem 5) = 13

step 3

Calculate the percentile rank using the formula: $\text{Percentile} = \left( \frac{\text{Number of values below 5.2}}{\text{Total number of values}} \right) \times 100$ Substituting the values: $\text{Percentile} = \left( \frac{13}{35} \right) \times 100 \approx 37.14$

Answer

A

Key Concept

Percentile Calculation

Explanation

The percentile rank is calculated by determining the proportion of data points below the given value and multiplying by 100.

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