What is the standard deviation of 1 | 6
2 |
3 | 4 9
4 | 0 1 4 8
5 | 0 1 5 6 9
6 | 2 3 3 6

To calculate the **standard deviation** from the given data set, we will:

1. Expand the stem-and-leaf plot into actual numbers.
2. Calculate the mean (average) of the data.
3. Compute the squared differences from the mean.
4. Find the variance (the average of these squared differences).
5. Take the square root of the variance to get the standard deviation.

### 1. Expand the stem-and-leaf plot:

- **1 | 6** → 16
- **2 |** → No leaves (no values in the 20s)
- **3 | 4 9** → 34, 39
- **4 | 0 1 4 8** → 40, 41, 44, 48
- **5 | 0 1 5 6 9** → 50, 51, 55, 56, 59
- **6 | 2 3 3 6** → 62, 63, 63, 66

### Expanded data set:
16, 34, 39, 40, 41, 44, 48, 50, 51, 55, 56, 59, 62, 63, 63, 66

Now, let's calculate the mean and standard deviation.The mean (average) of the data set is approximately **49.19**, and the standard deviation is approximately **12.81**.

Would you like more details on the steps, or do you have any further questions?

Here are 5 related questions to explore:
1. How is variance related to standard deviation?
2. What is the difference between population and sample standard deviation?
3. How does changing the data set affect the standard deviation?
4. Can standard deviation ever be negative?
5. How would you calculate the standard deviation if you had grouped data?

**Tip:** The standard deviation measures how spread out the values in a data set are. A higher standard deviation indicates greater variability.

Learn how to calculate the standard deviation from a stem-and-leaf plot. The expanded data set includes values such as 16, 34, 39, and others. The mean of the data is approximately 49.19, and the standard deviation is about 12.81. Suitable for students in Grades 9-12, this problem introduces key statistical concepts like mean, variance, and standard deviation.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation