# Standard deviation calculator

For standard deviation calculation, please enter numerical data separated with comma (or space, tab, semicolon, or newline). For example: 293.1 281.8 379.7 -848.1 -966.9 -540.0 725.0 -964.0 648.9 532.5 478.8 718.6 335.6## Calculation:

Statistical file:{63, 65, 68, 69, 69, 72, 75, 76, 77, 79, 79, 80, 82, 83, 84, 88, 90}

**Standard deviation σ=7.63165870128**

Corrected sample standard deviation s=7.86653373101

Corrected sample standard deviation s=7.86653373101

**Other statistical characteristics:**

Average (mean): μ=76.4117647059

Absolute deviation: 108.588235294

Mean deviation: 6.3875432526

Minimum: 63

Maximum: 90

Variance: 58.2422145329

Standard deviation σ=7.63165870128

Corrected sample standard deviation s=7.86653373101

Coefficient of variation c

_{V}=0.102949248212

Signal-to-noise ratio SNR=9.7135240652

Median: 77

Quartile Q1: 69

Quartile Q2: 77

Quartile Q3: 82.5

1st decile: 66.5

**(Too few data to calculate deciles)**

2nd decile: 68.5

3rd decile: 70.5

4th decile: 75.5

5th decile: 77

6th decile: 79

7th decile: 81

8th decile: 83.5

9th decile: 86

Interquartile range IQR: 13.5

Quartile Deviation QD: 6.75

Coefficient of Quartile Deviation CQD: 0.0891089108911

Lower fence: 48.75

Upper fence: 102.75

Set of outliers: {} - empty set - no outliers found

Interdecile range IDR: 19.5

Mode: {79, 69} - multimodal

Geometric mean: 76.0264454417

Harmonic mean: 75.6377719308

Sum: 1299

Sum of squares: 990.117647059

Sum of absolute values: 1299

Average absolute deviation: 6.3875432526

Range: 27

Frequency table :

element | frequency | cumulative frequency | relative frequency | cumulative relative frequency |
---|---|---|---|---|

63 | 1 | 1 | 0.0588235294118 | 0.0588235294118 |

65 | 1 | 2 | 0.0588235294118 | 0.117647058824 |

68 | 1 | 3 | 0.0588235294118 | 0.176470588235 |

69 | 2 | 5 | 0.117647058824 | 0.294117647059 |

72 | 1 | 6 | 0.0588235294118 | 0.352941176471 |

75 | 1 | 7 | 0.0588235294118 | 0.411764705882 |

76 | 1 | 8 | 0.0588235294118 | 0.470588235294 |

77 | 1 | 9 | 0.0588235294118 | 0.529411764706 |

79 | 2 | 11 | 0.117647058824 | 0.647058823529 |

80 | 1 | 12 | 0.0588235294118 | 0.705882352941 |

82 | 1 | 13 | 0.0588235294118 | 0.764705882353 |

83 | 1 | 14 | 0.0588235294118 | 0.823529411765 |

84 | 1 | 15 | 0.0588235294118 | 0.882352941176 |

88 | 1 | 16 | 0.0588235294118 | 0.941176470588 |

90 | 1 | 17 | 0.0588235294118 | 1 |

Count items: 17

Calculation of normal distribution

Sorted statistic file: {63, 65, 68, 69, 69, 72, 75, 76, 77, 79, 79, 80, 82, 83, 84, 88, 90}

### How to enter data as a frequency table?

Simple. First-type data elements (separated by spaces or commas, etc.), then type f: and further write frequency of each data item. Each element must have defined frequency that count of numbers before and after symbol f: must be equal. For example:1.1 2.5 3.99

f: 5 10 15

### How to enter a grouped data?

Grouped data are data formed by aggregating individual data into groups so that a frequency distribution of these groups serves as a convenient means of summarizing or analyzing the data.group | frequency |

10-20 | 5 |

20-30 | 10 |

30-40 | 15 |

10-20 20-30 30-40

f: 5 10 15

### How to enter data as a cumulative frequency table?

Similar as frequency table, but instead f: type cf: in second line. For example:10 20 30 40 50 60 70 80

cf: 5 13 20 32 60 80 90 100

The cumulative frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors. The last value will always be equal to the total for all observations since all frequencies will already have been added to the previous total.