# R Max and Min

## Max Min

In the previous chapter, we introduced the mtcars data set. We will continue to use this data set throughout the next pages.

You learned from the R Math chapter that R has several built-in math functions. For example, the `min()` and `max()` functions can be used to find the lowest or highest value in a set:

### Example

Find the largest and smallest value of the variable `hp` (horsepower).

Data_Cars <- mtcars

max(Data_Cars\$hp)
min(Data_Cars\$hp)

Result:

``` [1] 335 [1] 52 ```
Try it Yourself »

Now we know that the largest horsepower value in the set is 335, and the lowest 52.

We could take a look at the data set and try to find out which car these two values belongs to:

#### Observation of cars

```                     mpg cyl  disp  hp drat    wt  qsec vs am gear carb
Mazda RX4           21.0   6 160.0 110 3.90 2.620 16.46  0  1    4    4
Mazda RX4 Wag       21.0   6 160.0 110 3.90 2.875 17.02  0  1    4    4
Datsun 710          22.8   4 108.0  93 3.85 2.320 18.61  1  1    4    1
Hornet 4 Drive      21.4   6 258.0 110 3.08 3.215 19.44  1  0    3    1
Hornet Sportabout   18.7   8 360.0 175 3.15 3.440 17.02  0  0    3    2
Valiant             18.1   6 225.0 105 2.76 3.460 20.22  1  0    3    1
Duster 360          14.3   8 360.0 245 3.21 3.570 15.84  0  0    3    4
Merc 240D           24.4   4 146.7  62 3.69 3.190 20.00  1  0    4    2
Merc 230            22.8   4 140.8  95 3.92 3.150 22.90  1  0    4    2
Merc 280            19.2   6 167.6 123 3.92 3.440 18.30  1  0    4    4
Merc 280C           17.8   6 167.6 123 3.92 3.440 18.90  1  0    4    4
Merc 450SE          16.4   8 275.8 180 3.07 4.070 17.40  0  0    3    3
Merc 450SL          17.3   8 275.8 180 3.07 3.730 17.60  0  0    3    3
Merc 450SLC         15.2   8 275.8 180 3.07 3.780 18.00  0  0    3    3
Cadillac Fleetwood  10.4   8 472.0 205 2.93 5.250 17.98  0  0    3    4
Lincoln Continental 10.4   8 460.0 215 3.00 5.424 17.82  0  0    3    4
Chrysler Imperial   14.7   8 440.0 230 3.23 5.345 17.42  0  0    3    4
Fiat 128            32.4   4  78.7  66 4.08 2.200 19.47  1  1    4    1
Honda Civic         30.4   4  75.7  52 4.93 1.615 18.52  1  1    4    2
Toyota Corolla      33.9   4  71.1  65 4.22 1.835 19.90  1  1    4    1
Toyota Corona       21.5   4 120.1  97 3.70 2.465 20.01  1  0    3    1
Dodge Challenger    15.5   8 318.0 150 2.76 3.520 16.87  0  0    3    2
AMC Javelin         15.2   8 304.0 150 3.15 3.435 17.30  0  0    3    2
Camaro Z28          13.3   8 350.0 245 3.73 3.840 15.41  0  0    3    4
Pontiac Firebird    19.2   8 400.0 175 3.08 3.845 17.05  0  0    3    2
Fiat X1-9           27.3   4  79.0  66 4.08 1.935 18.90  1  1    4    1
Porsche 914-2       26.0   4 120.3  91 4.43 2.140 16.70  0  1    5    2
Lotus Europa        30.4   4  95.1 113 3.77 1.513 16.90  1  1    5    2
Ford Pantera L      15.8   8 351.0 264 4.22 3.170 14.50  0  1    5    4
Ferrari Dino        19.7   6 145.0 175 3.62 2.770 15.50  0  1    5    6
Maserati Bora       15.0   8 301.0 335 3.54 3.570 14.60  0  1    5    8
Volvo 142E          21.4   4 121.0 109 4.11 2.780 18.60  1  1    4    2
```

By observing the table, it looks like the largest hp value belongs to a Maserati Bora, and the lowest belongs to a Honda Civic.

However, it is much easier (and safer) to let R find out this for us.

For example, we can use the `which.max()` and `which.min()` functions to find the index position of the max and min value in the table:

### Example

Data_Cars <- mtcars

which.max(Data_Cars\$hp)
which.min(Data_Cars\$hp)

Result:

``` [1] 31 [1] 19 ```
Try it Yourself »

Or even better, combine `which.max()` and `which.min()` with the `rownames()` function to get the name of the car with the largest and smallest horsepower:

### Example

Data_Cars <- mtcars

rownames(Data_Cars)[which.max(Data_Cars\$hp)]
rownames(Data_Cars)[which.min(Data_Cars\$hp)]

Result:

``` [1] "Maserati Bora" [1] "Honda Civic" ```
Try it Yourself »

Now we know for sure:
Maserati Bora is the car with the highest horsepower, and Honda Civic is the car with the lowest horsepower.

## Outliers

Max and min can also be used to detect outliers. An outlier is a data point that differs from rest of the observations.

Example of data points that could have been outliers in the mtcars data set:

• If maximum of forward gears of a car was 11
• If minimum of horsepower of a car was 0
• If maximum weight of a car was 50 000 lbs

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