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How to compute standard deviation given a set of numbers?

Computation of standard deviation given a set of numbers, say 15, 18, 35, 56, 28

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  1. Calculator must be in SD mode (standard deviation mode) :Press [MODE] [.]
  2. However, if [FIX] or [SCI] appears on display you must press [MODE][9] first.
  3. Data input always starts with [SHIFT][SAC], to clear the registers of old data.
  4. Type a number and press the [DATA] key, it is the [M+] key at the bottom right of keypad.
After you finish entering the data

Press [SHIFT] [9] (sigma n-1) to get sample standard deviation
Press [SHIFT][8] (sigma n] for the population standard deviation
Press [SHIFT] [7] (xbar) for the mean
Press [SHIFT] [6] (n) for the number of data entries
Press [SHIFT] [5] (capital sigma x) for the sum of values
Press [SHIFT] [4] (capital sigma x to y) for the sum of squares of the values

For additional information you might consider taking a look at the calculator manual

Posted on Jun 22, 2010

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Related Questions:

1 Answer

How do you find themean absolute deviation?


The mean is the arithmetic average, so add up all the numbers and divide by the number of numbers.

The standard deviation is a little more involved. The formula and example are explained here:
Standard Deviation Formulas


Good luck.

Paul

May 07, 2015 | Office Equipment & Supplies

1 Answer

What is deviation standard


The standard deviation is a measure of how "tight" the samples are distributed around your mean.
In layman's terms, a small standard deviation indicates that most of your measurements are in the vicinity of the means; a large standard deviation corresponds to readings that are all over the place.
You could also say that the smaller the SD, the more your mean is representative of the data set.
For a better explanation, just look up Standard deviation on Wikipedia!

May 03, 2014 | Audio Players & Recorders

1 Answer

Deviation standard


For a sample this smaller size there are two std deviations. Sample std deviation s(n-1) = 0.550, and population std deviation s(n) = 0.541

Dec 22, 2013 | Audio Players & Recorders

1 Answer

How do I put my calculator in statistics mode?


The TI-30XA does not have to be switched to a statistics mode, the operations are available all the time. The choice of operations are somewhat limited; the calculator offers statistics functions for one dimensional data sets only (no linear interpolation of (x,y) value pairs, for example):
  • [2nd] [CSR] - erase statistics data
  • [mib8888_17.gif] - add a number to the sample set
  • [2nd] [mib8888_18.gif] - remove a number from the sample set
  • [2nd] [FRQ] - multiple entry of the same sample value
  • [2nd] [n] - sample set size
  • [2nd] [mib8888_19.gif] - sum of all sample elements
  • [2nd] [mib8888_20.gif] - sum of the squares of all sample elements
  • [2nd] [mib8888_21.gif] - average of the sample set
  • [2nd] [mib8888_22.gif] - standard deviation (sample set is a complete set)
  • [2nd] [mib8888_23.gif] - standard deviation (sample set is a subset of a larger set)
The calculator displays "STAT" if the current sample set is non-empty.

Example: calculate the average and standard deviation of the set { 3, 4, 5, 5, 5, 5, 6 }.
  1. [2nd] [CSR] - erase stat memory
  2. 3 [mib8888_17.gif] 4 [mib8888_17.gif] 5 [2nd] [FRQ] 4 [mib8888_17.gif] 6 [mib8888_17.gif] - enter the data, note the use of [2nd] [FRQ] to enter the four occurrences of "5". Entering 5 [mib8888_17.gif] four times would have done the same.
  3. [2nd] [mib8888_21.gif] - display the average of the set, (4.714...)
  4. [2nd] [mib8888_22.gif] - display the standard deviation of the set (0.8806...)

Jan 25, 2011 | Texas Instruments TI-30XA Calculator

1 Answer

Find the standard deviation of the following data set 5,5,5,5


The standard deviation is a measure on the variability of a number set from its average. Since all numbers in your set are the same, there is no variation from its average, and the standard deviation is 0.

Jan 25, 2011 | Texas Instruments TI-84 Plus Silver...

1 Answer

How do you find standard deviation on the calculator?


Press 2nd [CSR] (shift-7) to clear the statistical registers. Use the Sigma+ key (just above STO) to enter data points. Use 2nd [Sigma-] to remove erroneous data points. Use 2nd [sigma x n] (shift-divide) to compute the population standard deviation, or 2nd [sigma x n-1] (just to the left of the previous key) to compute the sample standard deviation.

Jun 07, 2010 | Texas Instruments TI-30XA Calculator

1 Answer

How do you enter frequencies for finding standard deviation? For example, Frequency=50, total of X or raw scores = 366.5. Summation of X squared =2836.39. What is standard deviation? How do you enter the...


Hello,
I am afraid I do not understand. The frequency of a PARTICULAR score is the number of times that particular value occurs in the data. It is not the number of data.
Ex: the data are:
4, 6, 5, 4, 4, 8, 9, 3, 3, 6, 7
Frequency of (3) =2
Frequency of (4)= 3
Frequency of (5) =1
Frequency of (6)= 2
Frequency of (7)=1
Frequency of (8)=1
Frequency of (9)=1

Number of data =11 (n=11)

You compute the mean M
M= (2x3 + 3x4 +1x5 +2x6+1x7+1x8+1x9) /11 =5.363636..
As you can see, if a term is not repeated it is multiplied by 1 (its frequency is one). Value 3 occurs twice (hence 2x3); value 4 occurs 3 times (3x4), etc.

To calculate by hand the sum of squares
3: (3-5.3636)^2 + (3-5.3636)^2 .................... = 2x(3-5.3636)^2
4: (4-5.3636)^2 + (4-5.3636)^2 +(4-5.3636)^2 = 3x(4-5.3636)^2
5: (5-5.3636)^2 ...................................... .= 1x(5-5.3636)^2
6: (6-5.3636)^2 +(6-5.3636)^2......................= 2x(6-5.3636)^2
7: (7-5.3636)^2.......................................... .=1x(7-5.3636)^2
8: (8-5.3636)^2......................................... ..=1x(8-5.3636)^2
9
: (9-5.3636)^2......................................... ..=1x(9-5.3636)^2
If I have not made a mistake the sum of squares is 40.5454

Standard Deviation
sd.jpg
The standard formula above gives s= square root (40.5454/10) =2.01
Population Standard Deviation
popsd.jpg
The population Standard deviation above is S= square root (40.5454/11) =1.9198

So if you perform the calculation with the calculator the only times you need to enter the frequency is for repeated terms. When you have to enter 6 above, its frequency is 2 you proceed as follows
6 [2nd][FRQ] 2 [Sigma+]

Once you entered the raw scores, the calculator does the rest.
Hope it helps.





Nov 06, 2009 | Texas Instruments TI-30XA Calculator

1 Answer

Standard Deviation


Press 2ND [CSR] to clear the stat data.

For each data point, enter the number followed by SIGMA+

If you have grouped data, enter the number followed by 2ND [FRQ] followed by the frequency then SIGMA+

Press 2ND [sigma x n] for the population standard deviation or 2ND [sigma x n-1] for the sample standard deviation.

May 25, 2009 | Texas Instruments TI-30X-IISTK Scientific...

1 Answer

Maths & statistic


Standard deviation is the average root mean squared deviation from the average of the numbers.

Familiarize yourself with the wikipedia page on standard deviation: http://en.wikipedia.org/wiki/Standard_deviation

In this case, your question is easy. The standard deviation is 0, so this means the boys ages are all the same.

So they're all 24/3 = 8 years old.

Proof:
8 + 8 + 8 = 24 <-- satisfies the constraint that the boys ages must total to 24.

Get the standard deviation of these numbers;

8+8+8 / 3 = 8 <-- the average value is 8

The deviation of each boy's age from the average is:
boy 1
--------
8 years old, which deviates from 8 by 0
boy 2
--------
8 years old, which deviates from 8 by 0
boy 3
--------
8 years old, which deviates from 8 by 0

So the deviations are 0, 0 and 0.

To get the standard deviation, you sum the squares of the deviations of each boy, get the average, and square root. So:

0² + 0² + 0² = 0
Average is 0 / 3 = 0
Square root of 0 = 0

So the standard deviation is 0. Which shouldn't be much of a surprise to you. We just had to actually DO the work to show that it was in fact 0.

Feb 08, 2008 | Audio Players & Recorders

2 Answers

Standard Deviations


This calc will do standard deviations. In the manual it is on page 2 and also on page 40.

Sep 07, 2006 | Casio FX-7400G Plus Calculator

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