# The pizza Palace recorded the number of extra toppings added to each pizza. a. Compute the Standard deviation. b. Compute the mean Round off the answer to three decimal places. 0 1 2 3 Number of Toppings 5 15 30 40 Percentage of Purchaces.

## Answer:

**a. Compute the Standard deviation.**

**Step 1: Find the mean**

The mean is the sum of all the values divided by the number of values.

```
Mean = (0 * 5 + 1 * 15 + 2 * 30 + 3 * 40) / (5 + 15 + 30 + 40) = 1.75
```

**Step 2: Find the squared deviations from the mean**

The squared deviation from the mean is the difference between a value and the mean, squared.

Number of toppings | Value | Deviation from the mean | Squared deviation from the mean |
---|---|---|---|

0 | 5 | -1.75 | 3.0625 |

1 | 15 | -0.75 | 0.5625 |

2 | 30 | 0.25 | 0.0625 |

3 | 40 | 0.75 | 0.5625 |

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**Step 3: Find the variance**

The variance is the average of the squared deviations from the mean.

```
Variance = (3.0625 + 0.5625 + 0.0625 + 0.5625) / 4 = 1.0625
```

**Step 4: Find the standard deviation**

The standard deviation is the square root of the variance.

```
Standard deviation = sqrt(1.0625) = 1.03
```

**Therefore, the standard deviation is 1.03.**

**b. Compute the mean**

The mean is the sum of all the values divided by the number of values.

```
Mean = (0 * 5 + 1 * 15 + 2 * 30 + 3 * 40) / (5 + 15 + 30 + 40) = 1.75
```

**Therefore, the mean is 1.75.**

**Summary**

- Standard deviation: 1.03
- Mean: 1.75