# Normal Probability Plot Maker

**
Instructions:
**
Use this Normal Probability Plot maker by entering the sample data below and this statistics calculator will provide step-by-step calculation of the required elements to construct the required probability plot.

## More About the Normal Probability Plot

A normal probability plot is a plot that is typically used to assess the normality of the distribution to which the passed sample data belongs to.

There are different types of normality plots (P-P, Q-Q and other varieties), but they all operate based on the same idea. The theoretical quantiles of a standard normal distribution are graphed against the observed quantiles.

Therefore, if the sample data comes from a
normality distributed population
, then the normal probability plot should look like a 45
^{
o
}
line, with random variations about it. If that is not the case, and the pattern of the normal probability
plot departs significantly/systematically from the normal probability plot, then one should suspect that
the distribution is not normal.

### How do you compute a normal probability plot?

There are several concrete steps you need to take, in a specific order to construct a normal probability plot

- In this concrete case, the data are ordered in ascending order, and we call such data as \(X_1, X_2, ...., X_i , ...., X_n\).
- For each \(X_i\) in this sequence of ordered data, we compute the theoretical frequencies \(f_i\), which are approximated using the following formula: \[ f_i = \frac{i - 0.375}{n + 0.25} \] (where \(i\) corresponds to the position in the ordered dataset)
- We then we also compute \(z_i\), is corresponding associated z-score as \[ z_i = \Phi^{-1}(f_i)\]
- Then, the normal probability plot is obtained by plotting the ordered X-values (your sample data) on the horizontal axis, and the corresponding \(z_i\) values on your vertical axis.

### Normal probability plot Excel

You can plot a normal probability graph in Excel, but it takes some time. Yo

### Calculators for the normal distribution and others

Other chart makers you can use are our normal distribution grapher , scatter plot maker or our Pareto chart maker .

### Example: Calculation of a normal probability plot

**Question**: You are provided with the following sample data: 2, 3, 4, 3, 3, 2, 3, 4, 5, 3, 2, 3, 1, 2, 3, 4, 5, 6, 3, 2, 4, 5,
6 10 10 10 12 12 1 2 3 3 and 23. Construct a normal probability plot.

Solution:

We need to construct a normal probability plot. These are the sample data that have been provided:

Observation: |
\(X\) |

1 | 2 |

2 | 3 |

3 | 4 |

4 | 3 |

5 | 3 |

6 | 2 |

7 | 3 |

8 | 4 |

9 | 5 |

10 | 3 |

11 | 2 |

12 | 3 |

13 | 1 |

14 | 2 |

15 | 3 |

16 | 4 |

17 | 5 |

18 | 6 |

19 | 3 |

20 | 2 |

21 | 4 |

22 | 5 |

23 | 6 |

24 | 10 |

25 | 10 |

26 | 10 |

27 | 12 |

28 | 12 |

29 | 1 |

30 | 2 |

31 | 3 |

32 | 3 |

33 | 23 |

The theoretical frequencies \(f_i\) need to be computed as well as the associated z-scores \(z_i\), for \(i = 1, 2, ..., 33\):

Observe that the theoretical frequencies \(f_i\) are approximated using the following formula:

\[ f_i = \frac{i - 0.375}{n + 0.25} \]where \(i\) corresponds to the position in the ordered dataset, and \(z_i\) is corresponding associated z-score. This iscomputed as

\[ z_i = \Phi^{-1}(f_i)\]The following table is obtained

Position (i) |
X (Asc. Order) |
f_{i} |
z_{i} |

1 | 1 | 0.0188 | -2.079 |

2 | 1 | 0.0489 | -1.656 |

3 | 2 | 0.0789 | -1.412 |

4 | 2 | 0.109 | -1.232 |

5 | 2 | 0.1391 | -1.084 |

6 | 2 | 0.1692 | -0.957 |

7 | 2 | 0.1992 | -0.844 |

8 | 2 | 0.2293 | -0.741 |

9 | 3 | 0.2594 | -0.645 |

10 | 3 | 0.2895 | -0.555 |

11 | 3 | 0.3195 | -0.469 |

12 | 3 | 0.3496 | -0.386 |

13 | 3 | 0.3797 | -0.306 |

14 | 3 | 0.4098 | -0.228 |

15 | 3 | 0.4398 | -0.151 |

16 | 3 | 0.4699 | -0.075 |

17 | 3 | 0.5 | 0 |

18 | 3 | 0.5301 | 0.075 |

19 | 4 | 0.5602 | 0.151 |

20 | 4 | 0.5902 | 0.228 |

21 | 4 | 0.6203 | 0.306 |

22 | 4 | 0.6504 | 0.386 |

23 | 5 | 0.6805 | 0.469 |

24 | 5 | 0.7105 | 0.555 |

25 | 5 | 0.7406 | 0.645 |

26 | 6 | 0.7707 | 0.741 |

27 | 6 | 0.8008 | 0.844 |

28 | 10 | 0.8308 | 0.957 |

29 | 10 | 0.8609 | 1.084 |

30 | 10 | 0.891 | 1.232 |

31 | 12 | 0.9211 | 1.412 |

32 | 12 | 0.9511 | 1.656 |

33 | 23 | 0.9812 | 2.079 |

The normal probability plot is obtained by plotting the X-values (your sample data) on the horizontal axis, and the corresponding \(z_i\) values on your vertical axis. The following normality plot is obtained: