Problem Overview:
The task involves creating a
stem-and-leaf plot for a set of data and then answering several statistical questions based on the plot. The data provided is the final grades in Mrs. Stein's Algebra I class:
89, 85, 75, 76, 63, 90, 88, 94, 71, 54, 95, 79, 83, 85.
#### Step 1: Understanding Stem-and-Leaf Plots
- A
stem-and-leaf plot is a way to organize numerical data where:
- The
stem represents the leading digit(s) (usually the tens place).
- The
leaf represents the trailing digit(s) (usually the ones place).
#### Step 2: Organizing the Data into a Stem-and-Leaf Plot
The given data is:
89, 85, 75, 76, 63, 90, 88, 94, 71, 54, 95, 79, 83, 85.
We will create the stem-and-leaf plot:
| Stem | Leaf |
|------|------|
| 5 | 4 |
| 6 | 3 |
| 7 | 1, 5, 6, 9 |
| 8 | 3, 5, 5, 8, 9 |
| 9 | 0, 4, 5 |
#### Step 3: Answering the Questions
##### Question 1: What is the range?
- The
range is the difference between the highest and lowest values in the dataset.
- Highest value: 95
- Lowest value: 54
- Range = \( 95 - 54 = 41 \)
##### Question 2: What is the mode?
- The
mode is the value that appears most frequently in the dataset.
- From the stem-and-leaf plot, we see that the number 85 appears twice, while all other numbers appear only once.
- Mode = 85
##### Question 3: What is the mean?
- The
mean is the average of all the values.
- Sum of all values:
\( 89 + 85 + 75 + 76 + 63 + 90 + 88 + 94 + 71 + 54 + 95 + 79 + 83 + 85 = 1142 \)
- Number of values: 14
- Mean = \( \frac{1142}{14} = 81.57 \) (rounded to two decimal places)
##### Question 4: What is the median?
- The
median is the middle value when the data is ordered.
- Ordered data:
Parent Tip: Review the logic above to help your child master the concept of stem leaf plots worksheet.
