# Statistics Summary Calculator

## Compute 5 number summary Min, Max, Quartiles (Q1, Q2 or Median, Q3) along with Mean, Mode, Variance, Standard Deviation, Standard Error and 3 sigma with histogram.

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Stats Calculator

Compute mean, median, std deviation - Enter your data as comma separated values or with spaces. You can also import csv or any data file with delimiters

## 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)

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 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)

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

## Histogram Chart

Class

Range

Frequency

1

0 - 43

0

2

44 - 87

3

3

88 - 131

2

4

132 - 175

0

5

176 - 219

2

6

220 - 263

2

7

264 - 307

0

8

308 - 351

0

9

352 - 395

1

10

396 - 439

0

11

440 - 483

1

12

484 - 527

0

Sigma

Empirical formula

Range

Frequency

%

1 sigma

mean - 1 * SD

mean + 1 * SD

55.8430 - 313.8490

8

66.7%

2 sigma

mean - 2 * SD

mean + 2 * SD

-73.1600 - 442.8520

11

91.7%

3 sigma

mean - 3 * SD

mean + 3 * SD

-202.1630 - 571.8550

12

100.0%

• 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)

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

### 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 ¯ )

where, n is Number of observations in sample, xi is individual values in sample and x ¯ is Sample mean

### Formula to calculate 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

### 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