24-27.
in-house certification exam
24. in which group was the person with the lowest score?
25. what was the median score for those in group-2?
26. what was the range of the data for group-1?
27. what percent of people in group-2 scored higher than 60?

Question

Accepted Answer

### Question 24
# Explanation:
## Step1: Analyze the box - plot for minimum scores
In a box - plot, the minimum score is represented by the bottom whisker or the lowest data point. For Group 1, the lowest data point (the dot at the bottom) is at 10. For Group 2, the lowest data point is at a value higher than 10 (around, say, 15 - 20). So we compare the minimum values of the two groups.
## Step2: Determine the group with the lowest score
Since the minimum score of Group 1 (10) is lower than the minimum score of Group 2, the person with the lowest score is in Group 1.
# Answer:
Group 1

### Question 25
# Explanation:
## Step1: Recall the definition of median in a box - plot
In a box - plot, the median is represented by the line inside the box. For Group 2, we look at the box - plot of Group 2 and find the line inside the box.
## Step2: Identify the median score for Group 2
From the box - plot of Group 2, the line inside the box (which represents the median) is at 60 (or around that value, but from the plot, it seems to be 60). Wait, no, looking at the box - plot of Group 2, the box has a line. Wait, maybe I misread. Wait, Group 2's box: the lower quartile, median, upper quartile. Wait, the box for Group 2: the median line is at 60? Wait, no, let's re - examine. Wait, the box for Group 2: the bottom of the box is at 50, the median line is at 60? Wait, no, maybe the median is 60? Wait, no, the box - plot for Group 2: the line inside the box (median) is at 60? Wait, actually, in a box - plot, the median is the middle line of the box. So for Group 2, the box has a line, let's see the y - axis. The y - axis has marks at 10,30,50,70,90. The box for Group 2: the bottom of the box is at 50, the median line is at 60? Wait, no, maybe the median is 60? Wait, no, maybe I made a mistake. Wait, the box for Group 2: the lower quartile (Q1) is at 50, the median (Q2) is at 60, and the upper quartile (Q3) is at 70? Wait, no, the box is from Q1 to Q3, and the median is inside. So looking at Group 2's box, the median line is at 60? Wait, no, maybe it's 60. Wait, actually, from the plot, Group 2's box: the median line is at 60. So the median score for Group 2 is 60.
# Answer:
60

### Question 26
# Explanation:
## Step1: Recall the formula for range
The range of a data set is calculated as $ \text{Range}=\text{Maximum value}-\text{Minimum value} $.
## Step2: Identify the maximum and minimum values for Group 1
For Group 1, from the box - plot, the maximum value (the top dot) is 90 and the minimum value (the bottom dot) is 10.
## Step3: Calculate the range for Group 1
Using the formula $ \text{Range}=90 - 10=80 $.
# Answer:
80

### Question 27
# Explanation:
## Step1: Recall the concept of quartiles and box - plot
In a box - plot, the box represents the middle 50% of the data (from Q1 to Q3), and the data above Q3 is 25% of the data (since the total data is divided into four quartiles: Q1 (25th percentile), Q2 (50th percentile, median), Q3 (75th percentile)). Wait, actually, the percentage of data above Q3 is 25%, and the data between the median and Q3 is 25%. Wait, no, let's think again. The box - plot: the data is divided into four parts. The bottom 25% is below Q1, 25% between Q1 and median, 25% between median and Q3, and 25% above Q3. Wait, no, actually, Q1 is the 25th percentile, Q2 is the 50th percentile (median), Q3 is the 75th percentile. So the percentage of data above Q3 is $ 100 - 75 = 25\% $, and the percentage of data between the median and Q3 is $ 75 - 50=25\% $. Wait, but we want the percentage of people in Group 2 who scored higher than 60. Wait, the median of Group 2 is 60? Wait, no, in question 25, we found the median of Group 2 is 60? Wait, no, maybe I made a mistake in question 25. Wait, let's re - examine Group 2's box - plot. The box for Group 2: the bottom of the box is at 50, the median line is at 60, and the top of the box is at 70. Wait, so the median is 60. So the data above the median (60) is 50%? Wait, no, the median is the 50th percentile. So data above the median is 50%? Wait, no, the median divides the data into two equal parts: 50% below the median and 50% above the median. Wait, but in a box - plot, the box is from Q1 to Q3 (25th to 75th percentile), and the median is inside. So if the median is 60, then the percentage of data above 60 is 50%? Wait, no, that's not right. Wait, the median is the middle value. So if we have a data set, half of the data is below the median and half is above. So if the median of Group 2 is 60, then 50% of the people in Group 2 scored higher than 60? Wait, no, that can't be. Wait, maybe I misread the median. Wait, let's look at the box - plot of Group 2 again. The box for Group 2: the lower quartile (Q1) is at 50, the median (Q2) is at 60, and the upper quartile (Q3) is at 70. So the data from Q1 (50) to Q3 (70) is the middle 50% of the data. The median is at 60. So the data above the median (60) is the data from 60 to the maximum. The maximum is, say, 80 (the top dot). Wait, no, the top dot is at 80? Wait, the y - axis has 90 as a mark, but the top dot for Group 2 is at 80? Wait, maybe my initial analysis was wrong. Wait, let's start over. The box - plot: the minimum is the bottom dot, Q1 is the bottom of the box, median is the line in the box, Q3 is the top of the box, and maximum is the top dot. For Group 2: minimum is at 20 (approx), Q1 is at 50, median is at 60, Q3 is at 70, maximum is at 80. Wait, no, the y - axis is marked at 10,30,50,70,90. So the bottom dot of Group 2 is at 20 (between 10 and 30), Q1 is at 50, median is at 60, Q3 is at 70, top dot is at 80 (between 70 and 90). So the median is 60. So the data above the median (60) is the data from 60 to 80. Since the median is the 50th percentile, the percentage of data above the median is 50%? Wait, no, the median is the middle value. So if we order the data, half of the data is less than or equal to the median and half is greater than or equal to the median. But in a box - plot, the median is the line inside the box. So if the median is 60, then 50% of the people scored higher than 60? Wait, no, that's not correct. Wait, the median is the middle value. So for example, if we have 100 data points, 50 are below or equal to the median, and 50 are above or equal to the median. But if we want the percentage of people who scored higher than 60 (not greater than or equal), we need to see the position of 60. Wait, 60 is the median. So the number of people who scored higher than 60 is equal to the number of people who scored lower than 60, assuming a symmetric distribution, but in a box - plot, the median is the middle. So if the median is 60, then 50% of the data is above 60 (since half is above and half is below). Wait, but that seems wrong. Wait, no, the median is the value where 50% of the data is below it and 50% is above it. So if the median is 60, then 50% of the people in Group 2 scored higher than 60.
Wait, maybe I made a mistake. Let's think about quartiles. Q1 is 25th percentile, Q2 (median) is 50th, Q3 is 75th. So the data above Q2 (median) is 50% of the data. So yes, 50% of the people in Group 2 scored higher than 60 (since the median is 60).
# Explanation:
## Step1: Recall the meaning of median in a data set
The median of a data set is the middle value when the data is ordered. In a box - plot, the median is represented by the line inside the box. For Group 2, the median (line inside the box) is at 60.
## Step2: Determine the percentage of data above the median
Since the median divides the data set into two equal - sized groups (50% of the data is below the median and 50% is above the median), 50% of the people in Group 2 scored higher than 60.
# Answer:
50%

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QUESTION IMAGE

Question

Explanation:

Question 24

Step1: Analyze the box - plot for minimum scores

Step2: Determine the group with the lowest score

Step1: Recall the definition of median in a box - plot

Step2: Identify the median score for Group 2

Step1: Recall the formula for range

Step2: Identify the maximum and minimum values for Group 1

Step3: Calculate the range for Group 1

Answer:

Question 25