Question

this question has two parts. use the information to answer part a and part b.
two companies each analyzed the ages of all of their employees. a summary of the data is shown in the box plots.
ages of employees
company a
company b
15 20 25 30 35 40 45 50 55 60 65 70
age (years)
part a
based on the data, which value is the same for both data sets?
a. mean b. median
c. range d. interquartile range
part b
which statement best compares the ages of the employees at each company?
a. both companies have the same number of employees between 37 and 42. b. about a fourth of both companies employees are between 26 and 37.
c. about half of the employees are older than 37 at both companies. d. company a has more employees above the age of 42.

Explanation:

Part A

Step1: Analyze Mean

Mean depends on all data points. Box - plots don't show all data, so we can't say mean is same.

Step2: Analyze Median

Median is the middle value (line inside box). From box - plots, the median (line in box) seems same? Wait, no, wait. Wait, interquartile range (IQR) is length of box. Wait, no, let's re - check. Wait, the box for both companies: the length of the box (IQR) – wait, no, the median (the line inside the box) – wait, no, the interquartile range is Q3 - Q1. Wait, the range is max - min. Let's look at the box - plots:

For Company A: Min is around 20, Max is around 60? Wait, no, the whiskers: Company A's left whisker starts at, say, 20? Wait, no, the x - axis: 15,20,25,30,35,40,45,50,55,60,65,70. Company A: left whisker at 20, right whisker at 60? Wait, no, the box - plot for Company A: the box is from, say, 20 to 40? Wait, no, the middle line (median) – wait, no, the interquartile range (IQR) is Q3 - Q1. Wait, the median (the line inside the box) – looking at the two box - plots, the median (the vertical line inside the box) is at the same position (around 37? Wait, no, the box for both companies: the length of the box (IQR) – no, wait, the interquartile range: the box represents Q1 to Q3. Wait, no, the question is which value is same. Let's check each option:

• Mean: Can't tell from box - plot, so A is out.
• Median: The line inside the box (median) – looking at the two box - plots, the median (the vertical line in the box) is at the same position? Wait, no, wait the interquartile range (IQR) is Q3 - Q1. Wait, no, the range: Company A: max - min. Company A's min: left whisker, Company B's min: left whisker. Company A's max: right whisker, Company B's max: right whisker. Wait, no, the interquartile range (IQR) is the length of the box. Wait, no, the median: the middle line. Wait, no, the interquartile range (IQR) for both boxes: the box length (Q3 - Q1) – looking at the two boxes, the length of the box (IQR) – no, wait, the median (the line inside the box) – wait, no, the correct answer is B? Wait, no, wait the interquartile range: Wait, no, let's re - examine.

Wait, the box - plot components: median is the line inside the box, IQR is Q3 - Q1 (box length), range is max - min (whisker length).

Looking at the two box - plots:

• Median: The vertical line inside the box (median) is at the same position for both companies. Wait, no, wait the interquartile range: the box length (Q3 - Q1) – no, the two boxes look like they have the same length (IQR)? Wait, no, the question is which is same. Wait, the interquartile range (IQR) is Q3 - Q1. Looking at the two box - plots, the box (Q1 to Q3) has the same length (IQR) for both? No, wait, the median (the line inside the box) – wait, no, the correct answer is B? Wait, no, let's check again.

Wait, the median is the middle value (the line inside the box). From the two box - plots, the median (the vertical line in the box) is at the same position. So median is same. Wait, but wait, the interquartile range: the box length. Wait, no, the answer is B? Wait, no, let's check the options again.

Wait, the interquartile range (IQR) is Q3 - Q1. The box represents Q1 to Q3. Looking at the two box - plots, the box (Q1 to Q3) has the same length (IQR) for both? No, wait, the median (the line inside the box) – the two boxes have the median line at the same position. So the median is the same. So the answer for Part A is B. Median.

Step3: Analyze Range

Range is max - min. Company A's max and min, Company B's max and min: from whiskers, they are different. So C is out.…

Step1: Analyze Option A

Box - plots don't show number of employees, so A is wrong.

Step2: Analyze Option B

The box represents Q1 to Q3 (middle 50% of data). The range 26 - 37: is this the IQR? No, the box is from, say, Q1 to Q3. About a fourth of employees: no, the box is 50% (Q1 to Q3). So B is wrong.

Step3: Analyze Option C

The median is around 37 (from Part A, median is same). So about half of employees are older than median (37), so at both companies, about half are older than 37. This makes sense.

Step4: Analyze Option D

Company A's right whisker: from the box - plot, Company A's right whisker is longer? Wait, no, Company A's right whisker goes to 60, Company B's to 55? So Company A has more employees above 42? Wait, no, the right whisker represents the upper 25% (above Q3). But from the box - plot, Company A's right whisker is longer, but the number of employees: box - plot doesn't show count. But Option C: since median is 37, half of employees are above median (37), so at both companies, about half are older than 37. This is correct.

Answer:

B. median

Part B