Standard deviation calculator

For standard deviation calculation, please enter numerical data separated with comma (or space, tab, semicolon, or newline). For example: -751.3 788.1 -289.3 510.8 227.8 707.0 346.9 972.4 342.2 -466.0 250.0 431.2 243.3

5 15 25 35 45 55 65 75 f:15 15 23 22 25 10 5 10

Recalculate  

Calculation:

Statistical file:
{5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 65, 65, 65, 65, 65, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75}

Standard deviation σ=19.757894624681
Corrected sample standard deviation s=19.837403576203




Other statistical characteristics:
Average (mean): μ=35.16
Absolute deviation: 1984
Mean deviation: 15.872
Minimum: 5
Maximum: 75
Variance: 390.3744
Standard deviation σ=19.757894624681
Corrected sample standard deviation s=19.837403576203
Coefficient of variation c_V=0.56420374221283
Signal-to-noise ratio SNR=1.7724093712636
Median: 35
Quartile Q1: 25
Quartile Q2: 35
Quartile Q3: 45
1st decile: 5
2nd decile: 15
3rd decile: 25
4th decile: 25
5th decile: 35
6th decile: 41
7th decile: 45
8th decile: 53
9th decile: 65
Interquartile range IQR: 20
Quartile Deviation QD: 10
Coefficient of Quartile Deviation CQD: 0.28571428571429
Lower fence: -5
Upper fence: 75
Set of outliers: {} - empty set - no outliers found
Interdecile range IDR: 60
Mode: 45 - unimodal
Geometric mean: 27.949705891315
Harmonic mean: 19.242013741989
Sum: 4395
Sum of squares: 48796.8
Sum of absolute values: 4395
Average absolute deviation: 15.872
Range: 70
Frequency table :

element	frequency	cumulative frequency	relative frequency	cumulative relative frequency
5	15	15	0.12	0.12
15	15	30	0.12	0.24
25	23	53	0.184	0.424
35	22	75	0.176	0.6
45	25	100	0.2	0.8
55	10	110	0.08	0.88
65	5	115	0.04	0.92
75	10	125	0.08	1

Z-score: {-1.5265, -1.5265, -1.5265, -1.5265, -1.5265, -1.5265, -1.5265, -1.5265, -1.5265, -1.5265, -1.5265, -1.5265, -1.5265, -1.5265, -1.5265, -1.0204, -1.0204, -1.0204, -1.0204, -1.0204, -1.0204, -1.0204, -1.0204, -1.0204, -1.0204, -1.0204, -1.0204, -1.0204, -1.0204, -1.0204, -0.5142, -0.5142, -0.5142, -0.5142, -0.5142, -0.5142, -0.5142, -0.5142, -0.5142, -0.5142, -0.5142, -0.5142, -0.5142, -0.5142, -0.5142, -0.5142, -0.5142, -0.5142, -0.5142, -0.5142, -0.5142, -0.5142, -0.5142, -0.0081, -0.0081, -0.0081, -0.0081, -0.0081, -0.0081, -0.0081, -0.0081, -0.0081, -0.0081, -0.0081, -0.0081, -0.0081, -0.0081, -0.0081, -0.0081, -0.0081, -0.0081, -0.0081, -0.0081, -0.0081, -0.0081, 0.498, 0.498, 0.498, 0.498, 0.498, 0.498, 0.498, 0.498, 0.498, 0.498, 0.498, 0.498, 0.498, 0.498, 0.498, 0.498, 0.498, 0.498, 0.498, 0.498, 0.498, 0.498, 0.498, 0.498, 0.498, 1.0042, 1.0042, 1.0042, 1.0042, 1.0042, 1.0042, 1.0042, 1.0042, 1.0042, 1.0042, 1.5103, 1.5103, 1.5103, 1.5103, 1.5103, 2.0164, 2.0164, 2.0164, 2.0164, 2.0164, 2.0164, 2.0164, 2.0164, 2.0164, 2.0164}
Count items: 125

Calculation of normal distribution

Sorted statistic file: {5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 65, 65, 65, 65, 65, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75}
Statistical file:
{5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 65, 65, 65, 65, 65, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75}

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.