A librarian records the number of books read by 25 students in a month: 5, 3, 8, 7, 6, 4, 6, 5, 3, 7, 8, 6, 5, 4, 7, 6, 5, 8, 4, 7, 6, 5, 8, 7, 4.  Compute for the Standard Deviation

To compute the standard deviation, we follow these steps:

1. **Find the Mean (Average):**

   \[
   \text{Mean} = \frac{\sum x_i}{n}
   \]
   where \(x_i\) are the individual values and \(n\) is the total number of values.

   The dataset: 5, 3, 8, 7, 6, 4, 6, 5, 3, 7, 8, 6, 5, 4, 7, 6, 5, 8, 4, 7, 6, 5, 8, 7, 4.

   \[
   \text{Mean} = \frac{5 + 3 + 8 + 7 + 6 + 4 + 6 + 5 + 3 + 7 + 8 + 6 + 5 + 4 + 7 + 6 + 5 + 8 + 4 + 7 + 6 + 5 + 8 + 7 + 4}{25}
   \]
   \[
   \text{Mean} = \frac{143}{25} = 5.72
   \]

2. **Compute the Variance:**

   Variance is given by:
   \[
   \text{Variance} = \frac{\sum (x_i - \mu)^2}{n}
   \]
   where \( \mu \) is the mean.

   Let's calculate \( (x_i - \mu)^2 \) for each value.

3. **Calculate the Standard Deviation:**

   Standard Deviation is the square root of the variance:
   \[
   \text{Standard Deviation} = \sqrt{\text{Variance}}
   \]

Let me calculate this for you.The mean number of books read is approximately 5.76. The variance is 2.34, and the standard deviation is approximately 1.53.

Would you like further details or explanations?

Here are five related questions to expand on this topic:
1. How does the variance relate to the standard deviation?
2. How would the results change if more students were added to the dataset?
3. What is the significance of a low or high standard deviation in data analysis?
4. Can the mean and standard deviation alone describe the entire distribution of the data?
5. How can outliers affect the calculation of standard deviation?

**Tip:** The standard deviation is a useful measure of how spread out the values in a dataset are from the mean.

A librarian records the number of books read by 25 students in a month: 5, 3, 8, 7, 6, 4, 6, 5, 3, 7, 8, 6, 5, 4, 7, 6, 5, 8, 4, 7, 6, 5, 8, 7, 4. Compute for the Standard Deviation.

Learn how to compute the standard deviation for a dataset representing the number of books read by 25 students in a month. This solution covers key statistical concepts like mean, variance, and standard deviation, suitable for Grades 9-12 students.

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