We are going to calculate the mean and standard deviation for the following set of sample data by hand. Round all values to 4 decimal places where possible. 11, 5, 3, 12, 4 a) Calculate the mean. (Add all the numbers and divide by 5) b) Fill in the table. (x – 7)? 3 12 c) Calculate the standard deviation. Total | Standard deviation: S = means sum п — 1

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## Calculating Mean and Standard Deviation

In this tutorial, we will learn how to calculate the mean and standard deviation for a sample dataset. Let’s take the following set of sample data and calculate the required values by hand, rounding all values to four decimal places where possible:

**Sample Data:**
11, 5, 3, 12, 4

### Step 1: Calculate the Mean
The mean (average) of a data set is found by adding all the numbers together and dividing by the number of data points. This can be expressed as follows:

\[
\bar{x} = \frac{\sum x}{n}
\]

Where:
- \(\sum x\) = sum of all data points
- \(n\) = number of data points

For our sample data:

\[
\bar{x} = \frac{11 + 5 + 3 + 12 + 4}{5}
\]

\[
\bar{x} = \frac{35}{5} = 7.0000
\]

### Step 2: Fill in the Table
Next, we will prepare a table to help us calculate the deviations of each data point from the mean, and the square of these deviations. The columns in the table are:
- \(x\): the data points
- \(x - \bar{x}\): the deviation of each data point from the mean
- \((x - \bar{x})^2\): the square of each deviation

| \(x\)  | \(x - \bar{x}\) | \((x - \bar{x})^2\) |
|-------|--------------|-----------------|
| 11    |              |                 |
| 5     |              |                 |
| 3     |              |                 |
| 12    |              |                 |
| 4     |              |                 |
| **Total** |              |                 |

Let’s fill in the missing values:

| \(x\)  | \(x - \bar{x}\) | \((x - \bar{x})^2\) |
|-------|--------------|-----------------|
| 11    | 4            | 16              |
| 5     | -2           | 4               |
| 3     | -4           | 16              |
| 12    | 5            | 25              |
| 4
Transcribed Image Text:## Calculating Mean and Standard Deviation In this tutorial, we will learn how to calculate the mean and standard deviation for a sample dataset. Let’s take the following set of sample data and calculate the required values by hand, rounding all values to four decimal places where possible: **Sample Data:** 11, 5, 3, 12, 4 ### Step 1: Calculate the Mean The mean (average) of a data set is found by adding all the numbers together and dividing by the number of data points. This can be expressed as follows: \[ \bar{x} = \frac{\sum x}{n} \] Where: - \(\sum x\) = sum of all data points - \(n\) = number of data points For our sample data: \[ \bar{x} = \frac{11 + 5 + 3 + 12 + 4}{5} \] \[ \bar{x} = \frac{35}{5} = 7.0000 \] ### Step 2: Fill in the Table Next, we will prepare a table to help us calculate the deviations of each data point from the mean, and the square of these deviations. The columns in the table are: - \(x\): the data points - \(x - \bar{x}\): the deviation of each data point from the mean - \((x - \bar{x})^2\): the square of each deviation | \(x\) | \(x - \bar{x}\) | \((x - \bar{x})^2\) | |-------|--------------|-----------------| | 11 | | | | 5 | | | | 3 | | | | 12 | | | | 4 | | | | **Total** | | | Let’s fill in the missing values: | \(x\) | \(x - \bar{x}\) | \((x - \bar{x})^2\) | |-------|--------------|-----------------| | 11 | 4 | 16 | | 5 | -2 | 4 | | 3 | -4 | 16 | | 12 | 5 | 25 | | 4
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