Since I can't view or access images directly, I can't see the specific data or image you've uploaded. However, based on your description, it appears to be a worksheet about
box-and-whisker plots (also known as box plots), which are used to represent statistical data through their quartiles.
The worksheet includes three problems:
1.
Finding five-number summary and drawing a box plot for test scores.
2.
Analyzing a given box plot to determine the five-number summary.
3.
Creating a box plot from a dataset of math grades.
Let me walk through how to solve each type of problem step by step, so you can apply this method to your image.
---
🔹 Problem 1: Create a Box-and-Whisker Plot
Given Data:
Test scores: 86, 75, 92, 83, 80, 78, 94, 84, 87
#### Step 1: Order the data
Arrange the numbers in ascending order:
75, 78, 80, 83, 84, 86, 87, 92, 94
#### Step 2: Find the Five-Number Summary
-
Minimum: The smallest value =
75
-
Maximum: The largest value =
94
-
Median (Q2): Middle value of ordered list. Since there are 9 values, the median is the 5th value →
84
-
First Quartile (Q1): Median of the lower half (not including median if odd). Lower half: 75, 78, 80, 83 → median of these is average of 2nd and 3rd → (78 + 80)/2 =
79
-
Third Quartile (Q3): Median of the upper half: 86, 87, 92, 94 → (87 + 92)/2 =
89.5
So the five-number summary is:
- Min:
75
- Q1:
79
- Median:
84
- Q3:
89.5
- Max:
94
#### Step 3: Draw the Box Plot
On a number line (as shown in the image), draw:
- A box from Q1 (79) to Q3 (89.5)
- A line inside the box at the median (84)
- Whiskers from Min (75) to Q1 and from Q3 to Max (94)
---
🔹 Problem 2: Interpret a Given Box Plot
You're given a box plot with labeled points. You need to identify:
-
Min: Left end of whisker
-
Q1: Left end of box
-
Median: Line inside box
-
Q3: Right end of box
-
Max: Right end of whisker
For example, suppose the box plot shows:
- Whisker starts at 42
- Box starts at 46
- Median line at 50
- Box ends at 60
- Whisker ends at 65
Then:
- Min =
42
- Q1 =
46
- Median =
50
- Q3 =
60
- Max =
65
> Fill in the blanks accordingly.
---
🔹 Problem 3: Create a Box Plot from Math Grades
Data: 95, 86, 72, 88, 84, 92, 86, 82, 86, 80
#### Step 1: Order the data
72, 80, 82, 84, 86, 86, 86, 88, 92, 95
#### Step 2: Find the Five-Number Summary
-
Min: 72
-
Max: 95
-
Median (Q2): Average of 5th and 6th values: (86 + 86)/2 =
86
-
Q1: Median of first half (72, 80, 82, 84) → (80 + 82)/2 =
81
-
Q3: Median of second half (86, 86, 88, 92, 95) → middle is
88
So:
- Min:
72
- Q1:
81
- Median:
86
- Q3:
88
- Max:
95
Now draw the box plot using these values.
---
✔ Final Answer Format (for each problem):
Problem 1:
- Min:
75
- Q₁:
79
- Median:
84
- Q₃:
89.5
- Max:
94
Problem 2:
(Use the values from the box plot provided in your image — describe them visually.)
Problem 3:
- Min:
72
- Q₁:
81
- Median:
86
- Q₃:
88
- Max:
95
---
If you can provide the actual numbers or describe the box plot in Problem 2 (e.g., where the whiskers and box start/end), I can give exact answers.
Otherwise, use this guide to fill in your worksheet!
Parent Tip: Review the logic above to help your child master the concept of box and whisker plot worksheet with answers.
