Standard deviation calculator

For standard deviation calculation, please enter numerical data separated with comma (or space, tab, semicolon, or newline). For example: 100.2 123.7 781.6 988.7 892.6 606.9 314.4 106.6 -428.2 157.9 -893.3 192.7 359.3

63,65,68,69,69,72,75,76,77,79,79,80,82,83,84,88,90

Recalculate  

Calculation:

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

Standard deviation σ=7.6316587012832
Corrected sample standard deviation s=7.8665337310137




Other statistical characteristics:
Average (mean): μ=76.411764705882
Absolute deviation: 108.58823529412
Mean deviation: 6.3875432525952
Minimum: 63
Maximum: 90
Variance: 58.242214532872
Standard deviation σ=7.6316587012832
Corrected sample standard deviation s=7.8665337310137
Coefficient of variation c_V=0.10294924821188
Signal-to-noise ratio SNR=9.7135240651966
Median: 77
Quartile Q1: 69
Quartile Q2: 77
Quartile Q3: 82.5
1st decile: 64.6 (Too few data to calculate deciles)
2nd decile: 68.6
3rd decile: 70.2
4th decile: 75.2
5th decile: 77
6th decile: 79
7th decile: 81.2
8th decile: 83.4
9th decile: 88.4
Interquartile range IQR: 13.5
Quartile Deviation QD: 6.75
Coefficient of Quartile Deviation CQD: 0.089108910891089
Lower fence: 48.75
Upper fence: 102.75
Set of outliers: {} - empty set - no outliers found
Interdecile range IDR: 23.8
Mode: {79, 69} - multimodal
Geometric mean: 76.026445441703
Harmonic mean: 75.637771930754
Sum: 1299
Sum of squares: 990.11764705882
Sum of absolute values: 1299
Average absolute deviation: 6.3875432525952
Range: 27
Frequency table :

element	frequency	cumulative frequency	relative frequency	cumulative relative frequency
63	1	1	0.058823529411765	0.058823529411765
65	1	2	0.058823529411765	0.11764705882353
68	1	3	0.058823529411765	0.17647058823529
69	2	5	0.11764705882353	0.29411764705882
72	1	6	0.058823529411765	0.35294117647059
75	1	7	0.058823529411765	0.41176470588235
76	1	8	0.058823529411765	0.47058823529412
77	1	9	0.058823529411765	0.52941176470588
79	2	11	0.11764705882353	0.64705882352941
80	1	12	0.058823529411765	0.70588235294118
82	1	13	0.058823529411765	0.76470588235294
83	1	14	0.058823529411765	0.82352941176471
84	1	15	0.058823529411765	0.88235294117647
88	1	16	0.058823529411765	0.94117647058824
90	1	17	0.058823529411765	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. Write data elements (separated by spaces or commas, etc.), then write f: and further write the frequency of each data item. Each element must have a defined frequency that counts numbers before and after symbol f: must be equal. For example:

1.1 2.5 3.99
f: 5 10 15

How to enter grouped data?

Grouped data are 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

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 to a frequency table, but instead, f: write cf: in the 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 equal the total for all observations since the calculator will have already added all frequencies to the previous total.