In a corporate evaluation of 200 employees, performance scores range from 0 to 100. An emp… — GMAT

In a corporate evaluation of $200$ employees, performance scores range from $0$ to $100$ . An employee with a score of $84$ scored strictly higher than $150$ employees and strictly lower than $42$ employees, while the remaining employees received a score of exactly $84$ . If the percentile rank of a score is defined as the percentage of all scores strictly below it plus half the percentage of all scores equal to it, what is the percentile rank of a score of $84$ ?

A
75th percentile
77th percentileAnswer
C
79th percentile
D
84th percentile
E
88th percentile

Answer

77th percentile

The correct answer represents the relative position of a score of 84. Since 150 employees scored lower and 8 employees scored equal to 84, applying the percentile formula yields ((150 + 4) / 200) * 100 = 77th percentile.

Step-by-Step Solution

Determine the number of employees scoring exactly 84.

Number of employees scoring 84 =

200 - 150 - 42 = 8

The total group size equals the sum of students scoring below 84, above 84, and equal to 84.

Calculate the effective count of scores at or below 84 under the given percentile definition.

Effective count =

150 + 0.5 \times 8 = 154

The definition specifies adding the count of strictly lower scores to half the count of tied scores.

Convert the effective count to a percentile rank.

Percentile rank =

\frac{154}{200} \times 100 = 77\text{th percentile}

Dividing by the total number of scores (

200

) and multiplying by

100

converts the count into a percentage.

Key Concept

Percentile Rank Calculation

Estimated Time:1m 30s

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