An analyst recorded the number of years of experience for 25 employees at a software compa… — SAT

An analyst recorded the number of years of experience for $25$ employees at a software company. The distribution of the employees' experience is shown in the table below:

Years of Experience	Number of Employees
$1$	$5$
$2$	$8$
$3$	$6$
$4$	$4$
$15$	$2$

If the $2$ employees with $15$ years of experience are removed from the dataset, which of the following statements is true?

The mean of the dataset will decrease, and the median of the dataset will remain the same.Answer
B
Both the mean and the median of the dataset will decrease.
C
The median of the dataset will decrease, and the mean of the dataset will remain the same.
D
The mean of the dataset will decrease, and the median of the dataset will increase.

Answer

The mean of the dataset will decrease, and the median of the dataset will remain the same.

Removing the two extreme values of

15

years of experience significantly reduces the sum of the data, causing the mean to decrease from

3.4

to approximately

2.39

. However, the median remains

2

because both the

13^{\text{th}}

value of the original

25

-element dataset and the

12^{\text{th}}

value of the new

23

-element dataset fall within the category of

2

years of experience.

Step-by-Step Solution

Calculate the initial mean and identify the initial median of the dataset.

Initial mean is

3.4

years, and initial median is

2

years.

To establish the baseline values. The total number of employees is

5 + 8 + 6 + 4 + 2 = 25

. The sum of the years of experience is

(1 \times 5) + (2 \times 8) + (3 \times 6) + (4 \times 4) + (15 \times 2) = 5 + 16 + 18 + 16 + 30 = 85

. The initial mean is

\frac{85}{25} = 3.4

. Since there are

25

data points, the median is the

13^{\text{th}}

data point when ordered. Cumulatively counting the frequencies: the first

5

values are

1

, and the next

8

values (positions

6

13

) are

2

. Therefore, the

13^{\text{th}}

value is

2

Calculate the new mean and identify the new median after removing the two employees with

15

years of experience.

New mean is approximately

2.39

years, and new median is

2

years.

To find the new measures of center after the outliers are removed. The new total number of employees is

25 - 2 = 23

. The new sum of experience is

85 - 30 = 55

. The new mean is

\frac{55}{23} \approx 2.39

. With

23

data points, the median is the

12^{\text{th}}

data point when ordered. Cumulatively, the first

5

values are

1

, and the next

8

values (positions

6

13

) are

2

. Therefore, the

12^{\text{th}}

value is still

2

Compare the initial and new values of the mean and median.

The mean decreases from

3.4

to approximately

2.39

, while the median remains

2

To determine which option correctly describes the relationship between the changes.

Key Concept

The mean is sensitive to extreme values (outliers) and changes when they are removed. The median is a resistant measure of center and remains unchanged if the middle position of the ordered data stays within the same value class.

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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