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







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 cV=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 :
elementfrequencycumulative frequencyrelative frequencycumulative 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
Z-score: {-1.7574, -1.4953, -1.1022, -0.9712, -0.9712, -0.5781, -0.185, -0.054, 0.0771, 0.3391, 0.3391, 0.4702, 0.7322, 0.8633, 0.9943, 1.5184, 1.7805}
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.

groupfrequency
10-205
20-3010
30-4015
This grouped data you can enter:
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.