## Statistical Analysis Result Table

Metric | Formula | Description | Result |
---|---|---|---|

Count | Count = n | n is the Number of items in dataset | 12 |

Sum | S = a1+a2+...+an | where, a1,a2,an, are data values | 2218.15 |

Min | Min = 1/2 (r+s-|r-s|) | where, r is first number and s is second number | 50.78 |

Max | Max = 1/2(r+s+|r-s|) | where, r is first number and s is second number | 469.82 |

Range | Range = Max - Min | where, max is maximum number, min is minimum number | 419.04 |

Mean | M = 1/n(a1+a2+...+an) | where, n is the number of observation and a1,a2,an are data values | 184.846 |

Median | M = [(n + 1) / 2]th term | where, n is the number of observation | 151.05 |

Mode | M = L + (fm-f1)h /(fm-f1)+(fm-f2) | where L = Lower limit Mode of modal class,fm = Frequency of modal class,f1 = Frequency of class preceding the modal class, f2= Frequency of class succeeding the modal class,h = Size of class interval | 378.32, 257.63, 469.82, 184.9, 50.78, 240.71, 57.35, 87.8, 117.2, 105.11, 53.82, 214.71 |

Quartile | Q1 = ((n+1)/4) Q2 = ((n+1)/2) Q3 = (3(n+1)/4) | where, q1 is first quartile, q2 is second quartile, q3 is third quartile and n is count numbers | 64.963 151.05 253.4 |

Outlier | U = q3 + 1.5 (q3-q1) L = q1 - 1.5 (q3-q1) | where, U is Upper Limit and L is Lower Limit and q1 and q3 are quartiles | none |

Variance | S2 = 1 n - 1 ∑ i = 1 n ( x i - x ¯ ) 2 | where, n is Number of observations in sample, xi is ith observation in the sample and x ¯ is Sample mean | 16641.75 |

Standard Deviation | S = 1 n - 1 ∑ i = Square root(1 n ( x i - x ¯ ) 2) | where, n is Number of observations in sample, xi is ith observation in the sample and x ¯ is Sample mean | 129.003 |

Standard Error | SE = SD/Square root(n) | where, SE is Standard Error, SD is standard deviation and n is total numbers | 37.24 |

Sample Variance | S2 = (1/ n - 1 ) * ∑ i( x i - x ¯ ) | where, n is Number of observations in sample, xi is individual values in sample and x ¯ is Sample mean | 18154.636 |

Sample Standard Deviation | S = Square root((1/ n - 1 ) * ∑ i( x i - x ¯ ) 2) | where, n is Number of observations in sample, xi is individual values in sample and x ¯ is Sample mean | 134.739 |

Sample Standard Error | SSE = SSD/Square root(n) | where, SSE is Sample Standard Error, SSD is sample standard deviation and n is total numbers | 38.896 |

## Population Statistics

In Population Statistics, the dataset represents the full data and the exact variance, standard deviation is calculated

Example is Scores of Students in a class, temperature recorded in a month

Population Statistics

Metric | Formula | Description | Result |
---|---|---|---|

Variance | S2 = 1 n - 1 ∑ i = 1 n ( x i - x ¯ ) 2 | where, n is Number of observations in sample, xi is ith observation in the sample and x ¯ is Sample mean | 16641.75 |

Standard Deviation | S = 1 n - 1 ∑ i = Square root(1 n ( x i - x ¯ ) 2) | 129.003 | |

Standard Error | SE = SD/Square root(n) | where, SE is Standard Error, SD is standard deviation and n is total numbers | 37.24 |

## Sample Statistics

In Sample Statistics, it represents a sampling of the data and that is used to project for an entire category

Example is Average Height of Male and Females in different countries

Sample Statistics

Metric | Formula | Description | Result |
---|---|---|---|

Sample Variance | S2 = (1/ n - 1 ) * ∑ i( x i - x ¯ ) | where, n is Number of observations in sample, xi is individual values in sample and x ¯ is Sample mean | 18154.636 |

Sample Standard Deviation | S = Square root((1/ n - 1 ) * ∑ i( x i - x ¯ ) 2) | 134.739 | |

Sample Standard Error | SSE = SSD/Square root(n) | where, SSE is Sample Standard Error, SSD is sample standard deviation and n is total numbers | 38.896 |

68-95-99.7 rule states that in a typical normal distribution, 68% of the data points fall within +/- 1 standard deviation of the mean.

95% within 2 standard deviation from the mean Almost 100% within 3 standard deviations from the mean

## Stats Formula

### Formula to calculate **Count**

Count = n

where n is the total number of items in the dataset

### Formula to calculate **Sum**

Sum = a1+a2+...+an

where, n is a1, a2, an, are data values

### Formula to calculate **Minimum**

Min = 1/2 (r+s-|r-s|)

where, r is first number and s is second number

### Formula to calculate **Maximum**

Max = 1/2 (r+s+|r-s|)

where, r is first number and s is second number

### Formula to calculate **Range**

Range = max-min

where, max is maximum number and min is minimum number

### Formula to calculate **Mean**

Mean = 1/n(a1+a2+...+an)

where, n is the number of observation and a1,a2,an are data values

### Formula to calculate **Median**

Median = [(n + 1) / 2]th term

where, n is the number of observation

### Formula to calculate **Mode**

Mode = L + (fm-f1)h /(fm-f1)+(fm-f2)

where, l is Lower limit Mode of modal class,fm is Frequency of modal class,f1 is Frequency of class preceding the modal class, f2 is Frequency of class succeeding the modal class,h is Size of class interval

### Formula to calculate **Quartile**

Q1 = ((n+1)/4)

Q2 = ((n+1)/2)

Q3 = (3(n+1)/4)

where, q1 is first quartile, q2 is second quartile, q3 is third quartile and n is integer numbers

### Formula to calculate **Outlier**

U = q3 + 1.5 (q3-q1)

L = q1 - 1.5 (q3-q1)

where, U is Upper Limit and L is Lower Limit and q1 is first quartile and q3 is third quartile

### Formula to calculate **Variance**

S2 = 1 n - 1 ∑ i = 1 n ( x i - x ¯ ) 2

where, n is Number of observations in dataset, xi is ith observation in the sample and x ¯ is mean

### Formula to calculate **Standard Deviation**

SD = 1 n - 1 ∑ i = Square root(1 n ( x i - x ¯ ) 2)

### Formula to calculate **Standard Error**

SE = SD/Square root(n)

where, SE is Standard Error, SD is standard deviation and n is total numbers

### Formula to calculate **Sample Variance**

S2 = (1/ n - 1 ) * ∑ i( x i - x ¯ )

### Formula to calculate **Sample Standard Deviation**

S = Square root((1/ n - 1 ) * ∑ i( x i - x ¯ ) 2)

### Formula to calculate **Sample Standard Error**

SSE = SSD/Square root(n)

where, SSE is Sample Standard Error, SSD is sample standard deviation and n is total numbers

### Formula to calculate **Sigma**

1 Sigma = Mean - 1 * Standard Deviation , Mean + 1 * Standard Deviation

2 Sigma = Mean - 2 * Standard Deviation , Mean + 2 * Standard Deviation

3 Sigma = Mean - 3 * Standard Deviation , Mean + 3 * Standard Deviation

### Formula to calculate **Class Interval Width**

CIW = SD / 3

where, SD is standard deviation