Casio FX-260 Solar
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Basic Statistics Operations on the CASIO fx 260
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FX 260 Training guide Tools FX 260 Solar Scientific Calculator Overhead OH 260 Applicable activities
Key Points/ Overview Basic scientific calculator Solar powered Ability to fix decimal places Backspace key to fix entry mistakes Single variable statistics The ONLY calculator that is GED approved Content Modes Basic Arithmetic Calculations Basic Functions and Operations Basic Calculations Constant Calculations Fraction calculations and simplification Percent calculations Powers and roots Internal Rounding Probability Random number generation Permutations and combinations Factorials Memory Memory Calculations Trigonometry Trigonometric/Inverse Trigonometric Functions Hyperbolic/ Inverse Hyperbolic Functions Coordinate Conversion Sexagesimal Functions (Degrees/Minutes/Seconds) Logarithmic Functions Statistics Entering and analyzing statistical data
References the Casio FX-260 Solar Users Guide Casio FX-260 Scientific calculator
FX 260 Training guide Modes Before starting a calculation, you must first enter the correct mode. To perform this type of calculation: Basic arithmetic calculations Standard deviation calculations Calculations using degrees Calculations using radians Calculations using grads Number of decimal place specification Number of significant digit specification Cancels FIX and SCI settings Perform this key operation: [MODE]  [MODE] [.] [MODE]  [MODE]  [MODE]  [MODE]  [x] (x = # of decimal places and ranges from 0 9) [MODE]  [x] (x = # of significant digits and ranges from 0 9) [MODE]  Name of mode: COMP SD DEG RAD GRA FIX
Display indicators show the current mode setting. If there is no display shown, this indicates COMP mode. The COMP and SD modes can be used in combination with the angle unit settings.
FX 260 Training guide
Basic Arithmetic Calculations Basic Functions and Operations The following are the basic functions and operations of the calculator. Backspaces and deletes the right digit of a displayed input value. [ON] [C] [SHIFT] Turns power on. Clears the displayed input value. Shifts the keyboard and accesses functions marked above the keys.
Note: There is no power off key.
Basic Calculations Be sure to press [AC] when beginning a new calculation. [+] [ - ] [x]  [=] [+/-] Addition, subtraction, multiplication, and division Performs calculation Changes the sign of a displayed value. You must enter the value first. Left and right parentheses. Note: The calculator uses order of operations. So for 2 + 3 x 4, you do not need parentheses around 3 x 4. The calculator will calculate 3 x 4, then add 2. This will input the numerical value for. Swaps the value of x and y in power and root calculations. Also swaps the minuend and subtrahend in subtraction calculations. Example: for 32, to swap 3 and 2, press  [xy]  [SHIFT] [X-Y] [=]. The answer displayed is 8.
[SHIFT]  [SHIFT] [X-Y]
FX 260 Training guide Constant calculations You can perform constant calculations by setting an automatic constant to continually add, subtract, multiply, or divide. Pressing [+], [ - ], [x], or  twice after inputting a number, will make that number a constant. K will be shown on the display, indicating that a constant is being used. For addition, enter [constant] [+] [+]. When you press [=], the constant will be added to the number on the display. Pressing [AC] clears the constant. Display For example:  [+] [+] [=] 4 Each time you press [=], it will add 2 to the displayed number  [+] [+]  [=]  [=]  [=] 13
Fraction calculations and simplification Use the COMP mode for fraction calculations. You can perform addition, subtraction, multiplication, and division. The result of a calculation that mixes fractions and decimal values is displayed as a decimal value. You can enter a fraction using the [a b/c] key. The total number of digits, including division marks, cannot exceed 10.
Be sure to press [AC] when beginning a new calculation. [a b/c] Inputs the integer part of a fraction (mixed number) and the numerator (b) /denominator (c) of a fraction in the form b/c. Example: to input , press  [a b/c] . Example: to input 2 , press  [a b/c]  [a b/c] . Converts the displayed value between mixed number and improper fraction. Converts the displayed value between fraction and decimal form.
NOTE: After entering a fraction using a b/c, pressing [=] will display it in simplest form.
FX 260 Training guide Percent calculations Use the COMP mode for percentage calculations. Example To find percentage of a number. 12% of 15  [x]  [SHIFT] [%] Display 1.8
To calculate percentage of one number to another. What percentage of 80 is 40?    [SHIFT] [%] To add a percentage. 15% to 1000 (or 1000 increased by 15%) To discount a percentage. 85 by 10% % change, when a value is increased From 30 to 36
 [x]  [SHIFT] [%] [+] 1150
 [x]  [SHIFT] [%] [-]
 [ - ]  [SHIFT] [%]
Percent of increase, when an amount is added. 300 cc is added to 500 cc  [+]  [SHIFT] [%]
Powers and roots [x2] [SHIFT] [x3] Squares a number. Example:  [x2 ] Cubes a number. Example:  [SHIFT] [x3] Raises a number to a power (other than 2 or 3). Example:  [xy]  [=] [SHIFT] [1/x] Calculates the reciprocal of the displayed value. Example:  [SHIFT] [1/x] [SHIFT] [ ] Calculates the square root of a number. Example:  [SHIFT] [ [SHIFT] [ 3 ] ]
Calculates the cube root of a number. Example:  [SHIFT] [ 3 ]
Calculates the specified root of a number. Example: For 271/3, press  [SHIFT] [x1/y]  [=]
FX 260 Training guide Internal Rounding Calculates internal rounding based on the number of decimal places you have on the display. For example, set the calculator to 3 fixed decimal places. Press    [=] Press [SHIFT] [RND]. This will truncate the number at 3 decimal places. Press [x]  [=] (The answer displayed is 399.994).
Probability Random number generation [SHIFT] [RAN#] Generates a random number between 0 and 0.999.
Permutations and combinations [SHIFT] [nPr] A permutation is a selection of objects in which the order matters. Example: To determine the number of possible different arrangements using 4 items selected from 10 items.  [SHIFT] [nPr]  [=] 5040 A combination is a selection of objects from a collection and order is irrelevant. Example: To determine the number of different combinations of 4 items selected from 10 items.  [SHIFT] [nCr]  [=] 210
Factorials [SHIFT] [x!] Calculates the factorial of a number. Example:  [SHIFT] [!]
FX 260 Training guide Memory Memory Calculations The memory function is convenient for calculating cumulative totals. [M+] Adds displayed value to memory. [MR] [SHIFT] [M-] [SHIFT] [Min] Recalls the value stored in memory. Subtracts the displayed value from memory. Replaces the current memory contents with the displayed value.
To clear memory, press  [SHIFT] [Min] or [AC] [SHIFT] [Min].
FX 260 Training guide Trigonometry Be sure to select the angle unit (D, R, G) you want to use before beginning a calculation. Mode 4 = Degrees (Deg) Mode 5 = Radians (Rad) Mode 6 = Grads (Gra) Trigonometric/Inverse Trigonometric Functions To calculate the sine, cosine, or tangent of the displayed angle. Example (in degree mode):  [sin] (=.5) To calculate the arcsine, arccosine, or arctangent. Example (in degree mode): [.5] [SHIFT] [sin] (= 30) Hyperbolic/ Inverse Hyperbolic Functions To calculate the hyperbolic sine, cosine, or tangent of the displayed angle. Example (in degree mode): [3.6] [hyp] [sin] (= 18.28545536) To calculate the hyperbolic arcsine, arccosine, or arctangent of the displayed angle. Example (in degree mode):  [hyp] [SHIFT] [sin -1] OR (= 4.094622224)  [SHIFT] [hyp] [sin -1] Coordinate Conversion You can convert between rectangular and polar coordinates. Make sure you are using the correct angle unit (D, R, G) before starting your calculation. [SHIFT] [R-P] Rectangular to polar coordinate conversion [SHIFT] [P-R] Polar to rectangular coordinate conversion [SHIFT] [X-Y] Use this operation to switch between the two coordinates produced by the conversion operation. Example: To convert polar coordinates (r = 2, = 60) to rectangular coordinates (x, y).  [SHIFT] [P-R]  [=] This gives you the x value. [SHIFT] [X-Y] This gives you the y value.
Degrees/Minutes/Seconds You can perform calculations using degrees, minutes, and seconds, and convert between sexagesimal and decimal values. Examples: Keystrokes [2.5] [=] Press [ o, , , ]  [ o, , , ]  [ o, , , ]  [ o, , , ] [x]  [=]
FX 260 Training guide Logarithmic Functions You can find logarithms, natural logarithms, and antilogarithms. [log] Calculates the common logarithm of the displayed value.  [log] Calculates the natural logarithm (base e) of the displayed value.  [ln] Calculates the common antilogarithm of the displayed value, which is 10 raised to the power of the value.  [SHIFT] [10x] Calculates the natural antilogarithm of the displayed value, which is e raised to the power of the value.  [SHIFT] [ex]
[ln] [SHIFT] [10x]
FX 260 Training guide Statistics Entering and analyzing statistical data Enter the statistics mode (SD) by pressing [MODE] [.]. Cancel FIX and SCI settings by pressing [MODE] . Pressing [MODE]  (Comp) exits the SD mode and clears all input data. [SHIFT] [SAC] Clears statistical memory. Be sure to perform this operation before inputting new data. Inputs the displayed value as data. Press [DATA] twice to input two entries of the same value. (NOTE: This is the M+ key). Deletes the displayed value as data.
Note: You can input multiple entries of the same data using [x]. To input 100 ten times, press  [x]  [DATA]
After entering data, you can retrieve the following values: [SHIFT] [ n-1] [SHIFT] [ n] [SHIFT] [ x ] [SHIFT] [n] [SHIFT] [x] [SHIFT] [x2] Sample standard deviation. Population standard deviation. Arithmetic mean. Number of data items. Sum of data. Sum of the squares.
Investigation 1: A Fundamental Difference Between the Mean and the Median
CALCULATORS: Casio: fx-260 Solar Casio: fx-260 Solar School
To enter data into the statistics register, press "MODE," then "." (the decimal point). You will see "SD" appear in the upper-right corner of the screen. Note the blue background around the statistics mode in the list of modes below the screen. All functions enclosed in blue brackets (above the 4 through 9 keys and the red AC key, and below the "M+" key) are only accessible when in the statistics mode. Even though the statistics register is clear when first entering the statistics mode, it is good practice to clear the register by pressing "SHIFT" and then "AC." This process accesses the function in yellow above the red "AC" key: Statistics All Clear. The register should be cleared each time a new exercise is begun. The following procedure enters the same value multiple times. Enter the value. Press the multiplication sign key. Enter the number of times the value is to be entered. Press the "M+" key. Both "DATA" and "DEL" appear enclosed in blue brackets beneath the "M+" key. "DATA" enters values into the data register. "DEL," which is in yellow and accessed using the "SHIFT" key, deletes values. When the calculator is in the statistics mode, these are the keystrokes for entering a value of M+ into the register 217 times: 1 NOTE: Entering M+ would enter the value 217 into the register one time. To enter a value multiple times, the value must precede the number of entries. The number of elements in the data register is represented by "n" which can be seen in yellow and enclosed in blue brackets above the "6" key. When all values in part 1 have been entered, the value for n should be 34140. Most of the values in the second part of the exercise are the same. Rather than clearing the register and starting anew, it is possible to delete the incorrect entries and preserve those that are correct. The procedure for deleting multiple entries is nearly identical to the procedure for entering. The only difference is that in the last step "SHIFT" must be pressed before "M+" so that the yellow function DEL can be accessed. When the entries in Part 1 of the exercise have been made, these are the keystrokes for deleting the 5114 entries of 9: 4 SHIFT M+ To exit the statistics mode, press
Casio, Inc. For Classroom Use Only
Part 1: The mean is approximately 7.32. 34140 students took the test. The median is 7. Part 2: The mean is approximately 7.36 The median is still 7. Part 3: Sample responses: The means are not the same. The first four heights are the same for both teams but the greatest heights are different. Therefore, the sums of the heights will be different. Each sum would be divided by 5 to get the mean of the heights, so the means will be different. The medians are the same. The heights are arranged from least to greatest, and the middle height for both teams is 6'3''.
Name ___________________________________________________ Date ______________
Student Worksheet Investigation 1
Part 1: The table below shows each score and its frequency for a 10-item tryout test of questions that are similar to those on the upcoming state mathematics exam. Tryout Scores Frequency Score 9 10
How many students took the test?
What is the mean of the data rounded to the nearest hundredth? What is the median of the data? ____________________
Part 2: The frequencies of the scores for 9 and 10 were recorded incorrectly. The correct scores are shown in the table below. Tryout Scores Frequency Score 9 10
What is the mean of the correct scores rounded to the nearest hundredth? _________________ Since the frequencies are the same, there is no change in the number of students that took the test. What is the median of the data? ____________________
This example illustrates the fact that the mean of a data set is affected by every value, but the median is not sensitive to a change in an extreme value.
Student Worksheet Investigation 1 (continued)
Part 3: The heights of the five starting basketball players on two teams are shown in the table below. Heights of Starting Basketball Players Team A Team B 5'9'' 5'9'' 6'1'' 6'1'' 6'3'' 6'3'' 6'7'' 6'7'' 6'9'' 7'1''
WITHOUT DOING ANY CALCULATION, answer the following questions. Are the means heights for the two teams the same? Explain why you think this is so. _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ Are the median heights for the two teams the same? Explain why you think this is so. _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________
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