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) $37^{ ext {th }}$ percentile
(B) $41^{ ext {st }}$ percentile
(c) $48^{ ext {th }}$ percentile
(D) $55^{ ext {th }}$ percentile

Question

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) $37^{	ext {th }}$ percentile
(B) $41^{	ext {st }}$ percentile
(c) $48^{	ext {th }}$ percentile
(D) $55^{	ext {th }}$ percentile

Accepted Answer

∻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: $$ ext{Percentile} = \left( \frac{ ext{Number of values below 5.2}}{ ext{Total number of values}} ight) imes 100 $$ Substituting the values: $$ ext{Percentile} = \left( \frac{13}{35} ight) imes 100 \approx 37.14 $$ ‖ ∻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.⚹◊What is the formula for calculating the percentile of a given value in a dataset?⍭ Generate me a similar question◊

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