# Statistics with R

In this post we will discuss about the statistics with R.

### Introduction

Statistics is a branch of mathematics working with data collection, organization, analysis, interpretation and presentation.Statistics is very important in Data Analysis ,Data Science and AI.

In this post we will learn about the descriptive statistics with R.

### Descriptive Statistics

Descriptive Statistics is used to summarize the data and it focuses on Distribution , the central tendancy and dispersion of the data . In this section we will learn to work on

• Distribution
• Central tendancy
• Dispersion

### Measures for central tendency

Central tendency is a measure that best summarizes the data and is a measure that is related to the center of the data set. Mean, median, and mode are the most common measures for central tendency.

We will use mtcars dataset from the datasets package in R.

 ``````1 `````` ``````head(mtcars) ``````
 ``````1 2 3 4 5 6 7 `````` `````` mpg cyl disp hp drat wt qsec vs am gear carb Mazda RX4 21.0 6 160 110 3.90 2.620 16.46 0 1 4 4 Mazda RX4 Wag 21.0 6 160 110 3.90 2.875 17.02 0 1 4 4 Datsun 710 22.8 4 108 93 3.85 2.320 18.61 1 1 4 1 Hornet 4 Drive 21.4 6 258 110 3.08 3.215 19.44 1 0 3 1 Hornet Sportabout 18.7 8 360 175 3.15 3.440 17.02 0 0 3 2 Valiant 18.1 6 225 105 2.76 3.460 20.22 1 0 3 1 ``````

### Mean

The mean is the average of the data. It is the sum of all data divided by the number of data points. mean() function gives the mean of the data.

 ``````1 2 `````` ``````## mean of the mpg column mean(mtcars\$mpg) ``````

 20.09062

### Median

The median is the Middle or midpoint of the data and is also the 50 percentile of the data. The median is not affected by the outliers and skewness of the data. median() function is used to get Median.

 ``````1 2 `````` ``````## median of the cyl median(mtcars\$cyl) ``````

 6

### Mode

Mode is a value in data that that is repeated more often than any other.

 ``````1 2 `````` ``````y <- table(mtcars\$gear) names(y)[which(y ==max(y))] ``````

 “3”

“3” is the mode of the gear column.

### Measures of variability

Measures of variability is the measures of the spread of the data. It can be range ,interquartile range, variance, standard deviation.

### Range

Range is the difference between the largest and smallest points in the data. range() function is used to find the range in R.

 ``````1 `````` ``````range(mtcars\$disp) ``````

 71.1 472.0

### Interquartile Range

The interquartile range is the measure of the difference between the 75 percentile or third quartile and the 25 percentile or first quartile. IQR() function is used to get interquartile Range in R.

 ``````1 2 `````` ``````## IQR of sugar IQR(mtcars\$wt) ``````

 1.02875

quantile() function is used to get quartiles in R.

 ``````1 2 `````` ``````## quartile of the sugar quantile(mtcars\$am) ``````
 ``````1 2 `````` `````` 0% 25% 50% 75% 100% 0 0 0 1 1 ``````

We can get the 25 and 75 percentiles of sugar in data.

 ``````1 `````` ``````quantile(mtcars\$mpg, 0.25) ``````
 ``````1 2 `````` `````` 25% 15.425 ``````
 ``````1 `````` ``````quantile(mtcars\$mpg, 0.75) ``````
 ``````1 2 `````` `````` 75% 22.8 ``````

### Variance

The variance is the average of squared differences from the mean and it is used to measure the spreadness of the data. var() function is used to find the sample variance in R.

 ``````1 `````` ``````var(mtcars\$mpg) ``````

 36.3241

var() and (N-1)/N is used to find the population variance.

 ``````1 2 `````` ``````N <- nrow(mtcars) var(mtcars\$mpg) * (N -1) / N ``````

 35.18897

### Standard Deviation

The standard deviation is the square root of a variance and it measures the spread of the data.

sd() is used to find the sample standard deviation of a dataset.

 ``````1 2 `````` ``````## standard deviation of the calcium sd(mtcars\$mpg) ``````

 6.026948

### Normal Distribution

Normal distribution is one of the most important theories because nearly all statistical tests require the data to be distributed normally. We can plot a distribution in R using hist() function.

 ``````1 `````` ``````hist(mtcars\$mpg, breaks = 15) `````` qqnorm() and qqline functions are used to find whether data is normally distributed.

 ``````1 2 `````` ``````qqnorm(mtcars\$mpg) qqline(mtcars\$mpg) `````` If the points do not deviate away from the line , the data is normally distributed.

### Modality

The modality of a distribution is determined by the number of peaks it contains.

 ``````1 `````` ``````hist(mtcars\$mpg, breaks = 15) `````` ### Skewness and Kurtosis

Skewness is a measurement of the symmetry of a distribution and how much the distribution is different from the normal distribution. Negative Skew is alos known as left skewed and positive skew is also known as right skewed. Th histogram from the previous section has a positive skew.

Kurtosis measures whether your dataset is heavy-tailed or light-tailed compared to a normal distribution. High Kurtosis means heavy tailed , so there are more outliers in the data. To find the kurtosis and skewness in R , we need moments package.

 ``````1 2 3 4 `````` ``````library(moments) ## skewness of the total_fat skewness(mtcars\$mpg) ``````

 0.6404399

 ``````1 2 `````` ``````## Kurtosis of the total fat kurtosis(mtcars\$mpg) ``````

 2.799467

### summary() and str() function

The summary() and str() function are the fastest ways to get descriptive statistics of the data. We can get the basic descriptive statistics using the summary() function.

 ``````1 `````` ``````summary(mtcars) ``````
 `````` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 `````` `````` mpg cyl disp hp Min. :10.40 Min. :4.000 Min. : 71.1 Min. : 52.0 1st Qu.:15.43 1st Qu.:4.000 1st Qu.:120.8 1st Qu.: 96.5 Median :19.20 Median :6.000 Median :196.3 Median :123.0 Mean :20.09 Mean :6.188 Mean :230.7 Mean :146.7 3rd Qu.:22.80 3rd Qu.:8.000 3rd Qu.:326.0 3rd Qu.:180.0 Max. :33.90 Max. :8.000 Max. :472.0 Max. :335.0 drat wt qsec vs Min. :2.760 Min. :1.513 Min. :14.50 Min. :0.0000 1st Qu.:3.080 1st Qu.:2.581 1st Qu.:16.89 1st Qu.:0.0000 Median :3.695 Median :3.325 Median :17.71 Median :0.0000 Mean :3.597 Mean :3.217 Mean :17.85 Mean :0.4375 3rd Qu.:3.920 3rd Qu.:3.610 3rd Qu.:18.90 3rd Qu.:1.0000 Max. :4.930 Max. :5.424 Max. :22.90 Max. :1.0000 am gear carb Min. :0.0000 Min. :3.000 Min. :1.000 1st Qu.:0.0000 1st Qu.:3.000 1st Qu.:2.000 Median :0.0000 Median :4.000 Median :2.000 Mean :0.4062 Mean :3.688 Mean :2.812 3rd Qu.:1.0000 3rd Qu.:4.000 3rd Qu.:4.000 Max. :1.0000 Max. :5.000 Max. :8.000 ``````

We can get the structure of the data using the str() function.

 ``````1 `````` ``````str(mtcars) ``````
 `````` 1 2 3 4 5 6 7 8 9 10 11 12 13 `````` ``````'data.frame': 32 obs. of 11 variables: \$ mpg : num 21 21 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 ... \$ cyl : num 6 6 4 6 8 6 8 4 4 6 ... \$ disp: num 160 160 108 258 360 ... \$ hp : num 110 110 93 110 175 105 245 62 95 123 ... \$ drat: num 3.9 3.9 3.85 3.08 3.15 2.76 3.21 3.69 3.92 3.92 ... \$ wt : num 2.62 2.88 2.32 3.21 3.44 ... \$ qsec: num 16.5 17 18.6 19.4 17 ... \$ vs : num 0 0 1 1 0 1 0 1 1 1 ... \$ am : num 1 1 1 0 0 0 0 0 0 0 ... \$ gear: num 4 4 4 3 3 3 3 4 4 4 ... \$ carb: num 4 4 1 1 2 1 4 2 2 4 ... ``````

This all about the basic or descriptive statistics with R.