Download Doing statistics problems with the Casio fx series calculators.

Doing statistics problems with the Casio fx series calculators.
There are two different varieties of Casio calculator, with several different model numbers. The simplest
and cheapest are the most direct, the more expensive ones slightly more complicated.
PART ONE: If the display shows only the numbers you’re entering as you enter them:
Across the top of the keyboard, you will find a table of numbers and the corresponding calculator mode.
The statistical mode is labelled SD. To enter this mode, press the MODE key, then the decimal [.] key. A
small SD should appear in the upper right-hand corner of the display.
Before you begin a new problem, press SHIFT (or INV) then AC. AC here stands for Accumulator Clear,
and this operation will clear any and all data you’ve previously entered.
To enter data, press the appropriate number keys for each data point, then press M+ to enter the data; repeat
for each data point.
Example: a sample has values, 14, 17.25, 89. To enter these data, press 1, then 4, then M+; press 1 then 7
then . then 2 then 5 then M+; press 8 then 9 then M+.
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To retrieve calculated values after entering all the data: Note that midway down the keyboard
there is a set of second functions for keys; these are labelled ⎯x, σn, σn-1, Σx2, Σx and n. Most often
these are second functions for number keys 7, 8, 9, 4, 5, 6 respectively.
To find the mean of the data you’ve entered, press SHIFT (or INV) then ⎯x (probably number key
7). With the three numbers above, the display should read 40.083333…
If the data you’ve entered are a population, to find the standard deviation, press SHIFT (or INV)
then σn (probably number key 8). For above, the display reads 34.614…
If the data you’ve entered are a sample, to find the standard deviation, press SHIFT (or INV) then
σn-1 (probably number key 9). For above, display reads 42.29423…
To find the variance, with the standard deviation in the display, press the x2 key. For sample
variance, the three numbers above yield 1797.2708…
Grouped Data: To enter the data for grouped data, press the midpoint then X (times) then the frequency,
then M+. Repeat for each class; retrieving the values proceeds normally.
Example:
Spending Range
No. of Students
mi
0-10
5
5
10-20
15
15
20-30
20
25
30-40
10
35
Place the calculator in SD mode and press SHIFT AC. Now, press 5X5 M+; 15X15 M+; 25X20 M+;
35X10 M+. Note carefully that the frequency must be the second number in each product term. If you
press SHIFT (or INV) n (probably the number 6 key), it will tell you how many values you’ve entered.
This is a quick check to see whether you’ve made some silly mistake. In this example, SHIFT n should
show 50. Read the mean and standard deviation as above. For this table, you should find ⎯x = 22, σn = 9, n
= 50.
If the data show the proportion in each range rather than the number simply multiply by the proportion then
press M+. For example, in the following table:
Number of Finishing Flaws
0–6
6 – 12
12 – 18
Percentage of Dishwasher Production
65
25
10
Midpoints
3
9
15
To find the mean number of flaws and standard deviation, enter 3 X .65 M+; 9X.25 M+; 15X.1 M+. Read
the mean and standard deviation as above. These would always be treated as population standard
deviations, even if they are samples because we don’t know the sample size.
PART TWO: If your calculator’s display has a line to show the operations you’re entering: typically, this
will apear as a line at the top of the display screen and will show the operation as you enter it. A simple
multiplication, say 12×6 should show as 12×6 as you enter it; finding the natural logarithm or should show
ln 27 and so on. (Calculators of this sort are generally a little more expensive than the simplest models
described above.)
Find the mode key at the top of the keyboard and press it. You will be presented with a menu; press the
number corresponding to SD (it’s probably 2). A small SD should appear, most likely at the bottom of the
display. Begin each calculation by pressing SHIFT then AC then =. You may have to press AC twice or it
may turn your calculator off. If so, turn it back on.
To enter data, press the appropriate number keys for each data point, then press M+ to enter the data; repeat
for each data point.
Example: a sample has values, 14, 17.25, 89. To enter these data, press 1, then 4, then M+; press 1 then 7
then . then 2 then 5 then M+; press 8 then 9 then M+.
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Retrieving calculated values after entering all the data depends on the calculator model. For some,
towards the bottom of the keyboard there is a set of second functions for keys; these are labelled
⎯x, σn, σn-1. These may also be labelled xσn and xσn-1. Press SHIFT then the key below the value
desired. With this type of calculator
o To find the mean of the data entered in the example, press SHIFT then ⎯x (probably
number key 1). With the three numbers above, the display should read 40.083333…
o If the data you’ve entered are a population, to find the standard deviation, press SHIFT
then σn or xσn (probably number key 2). For above, the display reads 34.614…
o If the data you’ve entered are a sample, to find the standard deviation, press SHIFT (or
INV) then σn-1 or xσn-1 (probably number key 3). For above, display reads 42.29423…
o To find the variance, with the standard deviation in the display, press the x2 key. For
sample variance, the three numbers above yield 1797.2708…
o NOTE: many Casio models of this type have keys labelled ⎯y, yσn, and yσn-1. These are
used for a different type of operation; just ignore them, but be sure not to confuse them
with the corresponding x keys.
Some other Casio models have a key at the top labelled S-VAR. Pressing this key causes a menu
to appear on the calculator’s display, with choices ⎯x, σn, and σn-1. Press the number
corresponding to the value desired, then press the = key. With this type of calculator
o To find the mean of the data entered in the example, press S-VAR, then select 1 from the
menu. With the three numbers above, the display should read 40.083333…
o If the data you’ve entered are a population, to find the standard deviation, press S-VAR
then select σn from the menu (probably by pressing number key 2). For above, the
display reads 34.614…
o If the data you’ve entered are a sample, to find the standard deviation, press S-VAR then
select σn-1 (probably number key 3). For above, display reads 42.29423…
o To find the variance, with the standard deviation in the display, press the x2 key. For
sample variance, the three numbers above yield 1797.2708…
With these more complex calculators, it is possible to calculate a mean and standard deviation from
grouped data, but it is probably not worth the trouble for the purposes of this course.