# Plot Z-Score in R

R supports powerful tools to plot z-score according to a given p-value. Thus, to learn about the z score we should know about the p-value. p-value and z scores are called statistical parameters and are used to make statistical calculations.

**p-value **is the probability of obtaining results at least as extreme as the observed result. Just like probability p-values lie between 0 and 1. If the Null hypothesis of a study comes out to be true then the p-value or calculated probability is the probability of finding the more extreme results.

**z-score** describes a value’s relationship to the mean of the group values. Let us take an example to understand the concept of z-score properly:

Consider a case of a class of 25 students. After the exams, the mean score of the class comes out to be 45. If we want to know whether a person who has scored 75 marks in the exam is among 10% of the scorers. In starting, it may seem to be a very tedious calculation. But by knowing the concept of z-scores it can become fairly easy.

**The formula for calculating z-score:**

- Standard deviation means how far the result is from the average value.
- Now a z score of 1 denotes that the observation is at a distance of one standard deviation towards right from the center.
- Similarly, a z score of -1 tells us that the observation is one standard deviation left from the center.

### Method 1: Naive approach

**Approach:**

- Create a vector and assign various values to it.
- Find the mean of the vector using function mean().
- Find the standard deviation using function sd().
- Subtract the mean value from the observation and divide the resultant with standard deviation.
- The vector obtained will have the required Z-score values.
- Now simply plot it.

**Example 1: **

## R

`# create vector` `a <- ` `c` `(9, 10, 12, 14, 5, 8, 9)` `# find mean` `mean` `(a)` `# find standard deviation` `sd` `(a)` `# calculate z` `a.z <- (a - ` `mean` `(a)) / ` `sd` `(a)` `# plot z-score` `plot` `(a.z, type=` `"o"` `, col=` `"green"` `)` |

**Output:**

**Example 2:**

## R

`# create vector` `a <- ` `c` `(7, 9, 2, 4, 25, 18, 19)` `# find mean` `mean` `(a)` `# find standard deviation` `sd` `(a)` `# calculate z-score` `a.z <- (a - ` `mean` `(a)) / ` `sd` `(a)` `# plot z-score` `plot` `(a.z, type=` `"o"` `, col=` `"green"` `)` |

**Output:**

**Method 2: Using qnorm()**

If we are given a p-value and our value is 0.70 then this means that it will be a point below which there are 80% of observations and 20% of observations lie above it. The easiest way for finding a z score if a p-value is given is to use qnorm() function. It takes the p-value as an argument and gives the z score as output.

**Syntax:**

qnorm(p-value)

**Approach:**

- Call qnorm() function with required p-value
- Plot z-score with the value so obtained

**Example :**

## R

`set <- ` `qnorm` `(0.75)` `plot` `(set, type=` `"o"` `, col=` `"green"` `)` |

**Output:**