42,35,43,22,33 find the standard deviation round the answer two decimal places

To calculate the standard deviation for the data set \(42, 35, 43, 22, 33\), follow these steps:

### Step 1: Find the Mean
The mean (\(\mu\)) is the sum of the data values divided by the number of data points.

\[
\mu = \frac{42 + 35 + 43 + 22 + 33}{5} = \frac{175}{5} = 35
\]

### Step 2: Find the Variance
For each data point, subtract the mean and square the result. Then find the average of these squared differences.

\[
\text{Variance} = \frac{(42 - 35)^2 + (35 - 35)^2 + (43 - 35)^2 + (22 - 35)^2 + (33 - 35)^2}{5}
\]

Now, let's calculate each squared difference:
\[
(42 - 35)^2 = 7^2 = 49
\]
\[
(35 - 35)^2 = 0^2 = 0
\]
\[
(43 - 35)^2 = 8^2 = 64
\]
\[
(22 - 35)^2 = (-13)^2 = 169
\]
\[
(33 - 35)^2 = (-2)^2 = 4
\]

So the variance is:
\[
\frac{49 + 0 + 64 + 169 + 4}{5} = \frac{286}{5} = 57.2
\]

### Step 3: Find the Standard Deviation
The standard deviation is the square root of the variance:

\[
\text{Standard Deviation} = \sqrt{57.2} \approx 7.56
\]

### Final Answer:
The standard deviation of the data set is approximately **7.56** (rounded to two decimal places).

Would you like any further explanation or details?

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Here are 5 related questions for further exploration:
1. How would the standard deviation change if one more data point is added?
2. What is the difference between population and sample standard deviation?
3. Can you calculate the variance of this data set?
4. What does a higher or lower standard deviation signify in a data set?
5. How do you calculate the standard deviation for grouped data?

**Tip:** The standard deviation measures the dispersion of data from the mean—higher values indicate greater variability.

42, 35, 43, 22, 33 find the standard deviation round the answer two decimal places

Learn how to calculate the standard deviation for the data set 42, 35, 43, 22, 33. This step-by-step solution covers key statistical concepts like mean, variance, and standard deviation. Suitable for students in Grades 9-12, this problem provides insight into data variability.

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