1. Three young boys have total age of 24. Answer the following questions with proper calculation steps and explanation.

If standard deviation of these boys’ ages is 0, what is the age of the oldest boy of the three?

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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.

Posted on Feb 08, 2008

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Posted on Jan 02, 2017

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Oct 24, 2017 | Math

Hey there,

You are looking for the cube root function which can be found under the MATH menu selection. the answer you get will simply need to be squared and you have your answer

You are looking for the cube root function which can be found under the MATH menu selection. the answer you get will simply need to be squared and you have your answer

Oct 03, 2013 | Texas Instruments TI-81 Calculator

The TI-83 can only convert a decimal to a fraction if the denominator has no more than three digits.

Try . 5 MATH FRAC

Does that give you 1/2?

Try . 5 MATH FRAC

Does that give you 1/2?

Sep 17, 2012 | Texas Instruments TI-83 Plus Calculator

The answer to this problem is 1728^(1/3). This is found by taking the appropriate root of both sides of the equation. You can enter this as follows in your calculator: as I have stated above(1728^(1/3), mind the brackets) or press MATH, scroll down or press 4 and enter 1728.
I hope I answered you question, the hardest part about this is understanding the math.

Jul 18, 2011 | Texas Instruments TI-84 Plus Calculator

first off you want you calculator in SD (standard deviation) mode to do this hit mode twice and then 1.

next it is good practice to start off by clearing the memory to do this hit shift, CLR,1 and then = this will clear statistical memory

to enter values into your data set , you enter the value, then press the DT (M+) button. (note: pressing DT repeatedly will impute the same value multiple times)

once you have finished pluging in your numbers your calculator can give you statistical information about the data set.

hitting shift then 1(S-SUM) gives you three options: 1 the sum of the squares of each value 2 the sum of each value 3 the number of terms in the data set hitting shift then 2 (S-VAR) gives you three more options 1 x bar (the mean) 2 x sigma n (the population standard deviation) 3 x sigma n-1 (the sample standard deviation)

you can use these tools to solve alot of statistical problems i hope this helped

Source: http://support.casio.com/pdf/004/fx115MS_991MS_E.pdf page 28 of he pdf

next it is good practice to start off by clearing the memory to do this hit shift, CLR,1 and then = this will clear statistical memory

to enter values into your data set , you enter the value, then press the DT (M+) button. (note: pressing DT repeatedly will impute the same value multiple times)

once you have finished pluging in your numbers your calculator can give you statistical information about the data set.

hitting shift then 1(S-SUM) gives you three options: 1 the sum of the squares of each value 2 the sum of each value 3 the number of terms in the data set hitting shift then 2 (S-VAR) gives you three more options 1 x bar (the mean) 2 x sigma n (the population standard deviation) 3 x sigma n-1 (the sample standard deviation)

you can use these tools to solve alot of statistical problems i hope this helped

Source: http://support.casio.com/pdf/004/fx115MS_991MS_E.pdf page 28 of he pdf

Dec 01, 2010 | Casio FX-300MSTP Scientific Calculator

The stdDev( function in the LIST MATH menu will calculate the standard deviation of a list. You can provide a second list if the data is grouped.

For detailed information refer to the "Lists", "Statistics", and "Infererential Statistics and Distribution" chapters in the guidebook. If you've misplaced your guidebook you can download a copy from

http://education.ti.com/educationportal/downloadcenter/SoftwareDetail.do?website=US&tabId=2&appId=6125

For detailed information refer to the "Lists", "Statistics", and "Infererential Statistics and Distribution" chapters in the guidebook. If you've misplaced your guidebook you can download a copy from

http://education.ti.com/educationportal/downloadcenter/SoftwareDetail.do?website=US&tabId=2&appId=6125

Sep 11, 2010 | Texas Instruments TI-84 Plus Calculator

Hello,

I am happy that you found my solution helpful and even flattered that you copied it in this thread. By doing this, you gave me the opportunity to discover an error in my post. In fact, the calculator does provide a column for the frequency. If you enter nothing in the frequency column, all data items will have their frequency set to 1, by default.

Back to the current subject: How to get the variance (the square of the standard deviation).

When you finish entering your data:

While the symbol xSigma_n or xSigma_n-1 is still displayed with the blinking cursor to its right, press the [x^2] key above the [HYP] key. The screen displays say xSigma_n ^2. Press [=] to calculate the variance.

As my motto says, I am always happy to help, but happier still when people show true appreciation.

Hope it helps.

I am happy that you found my solution helpful and even flattered that you copied it in this thread. By doing this, you gave me the opportunity to discover an error in my post. In fact, the calculator does provide a column for the frequency. If you enter nothing in the frequency column, all data items will have their frequency set to 1, by default.

Back to the current subject: How to get the variance (the square of the standard deviation).

When you finish entering your data:

- Press the [AC] button to exit the data editor.
- Press [****][STAT].
- Press [5:Var] to open the statistical result selection screen.
- Press [3: xSigma_n] or [4:xSigma_n -1] depending on what you are interested in (population or sample) standard deviation.
- The screen echoes the symbol for the value selected (the value displayed on the bottom line may be 0 or an old value from a previous calculation: it is not the value you have just calculated).
- Press [=] to display the current value of the SD chosen.
- By doing this you are in fact storing it it answer memory.
- All you have to do now is to raise it to power 2 by pressing the [x^2] key ( the one above the [HYP] key).
- The calculator will display Ans^2.
- Press [=] to display the value of the variance.

While the symbol xSigma_n or xSigma_n-1 is still displayed with the blinking cursor to its right, press the [x^2] key above the [HYP] key. The screen displays say xSigma_n ^2. Press [=] to calculate the variance.

As my motto says, I am always happy to help, but happier still when people show true appreciation.

Hope it helps.

Dec 11, 2009 | Casio fx-300ES Calculator

Hello,

Press [MATH][1:ToFrac] to convert an aswer to fraction.

If you enter 18.52[ToFrac] [ENTER gives 463/25

[MATH][2:ToDEC] converts a fraction to a decimal number.

Hope it helps.

Press [MATH][1:ToFrac] to convert an aswer to fraction.

If you enter 18.52[ToFrac] [ENTER gives 463/25

[MATH][2:ToDEC] converts a fraction to a decimal number.

Hope it helps.

Sep 22, 2009 | Texas Instruments TI-84 Plus Silver...

The [MODE] key can be used to select the modes described below.

Important! The following is a general explanation of Scientific Calculator modes. Note that your calculator may not include all of the modes described here.

1) Calculation Modes

Before performing a calculation, you first need to select the appropriate calculation mode.

COMP: Basic arithmetric calculations

(arithmetic operations, trigonometric functions, etc.)

COMPLEX: Complex number calculations

SD: Single-variable statistical calculations

(sample standard deviation, etc.)

LR or REG: Paired-variable statistical calculations

(linear regression statistical calculations, etc.)

BASE or BASE-n: Binary, octal, decimal, hexadecimal number system calculations

MAT: Matrix calculations (determinants, etc.)

VCT: Vector calculations

EQU: nth degree equations, simultaneous equations

2) Display Settings

Use these settings to control how calculation results are displayed.

Note that changing the Fix and Sci settings does not affect internal calculation results.

Norm: Exponential display format and cancels the currently configured Fix and Sci settings.

Fix: Specifies a fixed number of digits to the right of the decimal place.

Sci: Specifies a fixed number of significant digits.

3) Angle Unit Setting

(90°=?/2 radians=100 grads)

Deg: Degrees

Rad: Radians

Gra: Grads

4) Engineering Mode

Use this mode when you want to input and perform calculations using engineering symbols.

Please rate this response . .

Important! The following is a general explanation of Scientific Calculator modes. Note that your calculator may not include all of the modes described here.

1) Calculation Modes

Before performing a calculation, you first need to select the appropriate calculation mode.

COMP: Basic arithmetric calculations

(arithmetic operations, trigonometric functions, etc.)

COMPLEX: Complex number calculations

SD: Single-variable statistical calculations

(sample standard deviation, etc.)

LR or REG: Paired-variable statistical calculations

(linear regression statistical calculations, etc.)

BASE or BASE-n: Binary, octal, decimal, hexadecimal number system calculations

MAT: Matrix calculations (determinants, etc.)

VCT: Vector calculations

EQU: nth degree equations, simultaneous equations

2) Display Settings

Use these settings to control how calculation results are displayed.

Note that changing the Fix and Sci settings does not affect internal calculation results.

Norm: Exponential display format and cancels the currently configured Fix and Sci settings.

Fix: Specifies a fixed number of digits to the right of the decimal place.

Sci: Specifies a fixed number of significant digits.

3) Angle Unit Setting

(90°=?/2 radians=100 grads)

Deg: Degrees

Rad: Radians

Gra: Grads

4) Engineering Mode

Use this mode when you want to input and perform calculations using engineering symbols.

Please rate this response . .

Sep 08, 2009 | Casio MS-80TV Scientific Calculator

Hello,

In the main menu select [STAT] icon to enter Stat mode and display the statistical data lists. Use the satistical data lists to input data and perform statistical calculations. Use the arrows to move the highlighting around the lists.

Exemple: Enter the following values in List 1

1st line enter 90 [EXE]

2nd line 85 [EXE]

3 79 [EXE]

4 75 [EXE]

5 70 [EXE]

6 68 [EXE]

7 56 [EXE]

When finished you press [F2:Calc], then [F1:1Var] and the statistical results appear on screen.

Title of screen : 1-Variable

x bar =74.7142857

Capital Sigma x= 523

Capita Sigma X squared = 39851

x lower case sigma n = 10.5249945

x lower case sigma n-1= 11.3682934

n = 7

Scroll down with Down arrow to access other data

minX =56

Q1=68

Med =75

Q3=85

Xbar -x lower case sigma n =64.1892911

x bar + x lower case sigma n = 85.2392802

maxX=90

Mod=90

All you have to do now, is to look at the theory you learned and interpret what these values mean.

Hope it helps.

In the main menu select [STAT] icon to enter Stat mode and display the statistical data lists. Use the satistical data lists to input data and perform statistical calculations. Use the arrows to move the highlighting around the lists.

Exemple: Enter the following values in List 1

1st line enter 90 [EXE]

2nd line 85 [EXE]

3 79 [EXE]

4 75 [EXE]

5 70 [EXE]

6 68 [EXE]

7 56 [EXE]

When finished you press [F2:Calc], then [F1:1Var] and the statistical results appear on screen.

Title of screen : 1-Variable

x bar =74.7142857

Capital Sigma x= 523

Capita Sigma X squared = 39851

x lower case sigma n = 10.5249945

x lower case sigma n-1= 11.3682934

n = 7

Scroll down with Down arrow to access other data

minX =56

Q1=68

Med =75

Q3=85

Xbar -x lower case sigma n =64.1892911

x bar + x lower case sigma n = 85.2392802

maxX=90

Mod=90

All you have to do now, is to look at the theory you learned and interpret what these values mean.

Hope it helps.

Mar 09, 2009 | Casio CFX-9850G Plus Calculator

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