20.6k views
19 votes
A manager drew this box-and-whisker plot to represent the ages of her 23 employees. Every employee is a different age.

Box-and-whisker plot ranging from 34 to 58 with ticks at increments of 1. Plot defined by points at 35, 42, 49, 54, 57.

How many employees are older than 54 ..?

A manager drew this box-and-whisker plot to represent the ages of her 23 employees-example-1

2 Answers

6 votes

Answer: 6

Step-by-step explanation:

The left and right edges of the box represent Q1 and Q3 respectively

Q1 = first quartile

Q3 = third quartile

The boxplot shows Q3 = 54

The span from Q3 to the max represents exactly 25% of the population.

Take 25% of the 23 employees

0.25*23 = 5.75

Rounding to the nearest whole number leads to 6.

User Matthiasunt
by
3.5k points
11 votes

To determine how many employees are older than 54 from a box-and-whisker plot, we find that the upper quartile (Q3) is at age 54 and the maximum age is 57. Since 25% of 23 employees is approximately 6, and we exclude any employees of age 54, we infer there are 5 employees older than 54.

The question pertains to interpreting a box-and-whisker plot to determine how many employees are older than 54.

The box-and-whisker plot is used to represent the distribution of a dataset by identifying its quartiles and showing the spread of the values.

Given the plot points at 35, 42, 49, 54, and 57, we can infer that these represent the minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum of the data set, respectively.

Since the upper quartile (Q3) is at 54, and the maximum value is 57, all employees with ages between 54 (exclusive) and 57 (inclusive) fall into the highest 25% of the age range.

In a group of 23 employees, the top 25% would be approximately the last 6 employees when sorted by age, as 25% of 23 is about 5.75, which we round up to 6 since we are dealing with whole people.

However, since 54 is the age at which Q3 (upper quartile) is located, and we're interested in ages older than 54, we must exclude any employees of age 54.

Thus, the number of employees older than 54 would be the total number of employees in the final quartile minus any employees aged 54.

Given that every employee is a different age, if we have one employee aged 54, we subtract this from the 6 to get 5 employees who are older than 54.

User Getmemd
by
4.1k points