Casio Fx82LB Manual

							26  Mastering the calculator using the Casiofx-82LB
11.2 Mean and standard deviation of frequency distribution
Given below is the frequency table for the weights (kg) of a random sample of 30 first year 
university female students. Find the standard deviation, the variance and the mean.
The calculations needed to obtain the standard deviation without statistical keys for these data 
are:
Σx2 = 602 × 2 + 612 × 14 + 622 × 8 + 632 + 642 × 5 = 114 495
Σx = 60 × 2 + 61 × 14 + 62 × 8 + 63 + 64 × 5 = 1 853
s= 
= 
Thus:s= 1.2 kg and s2 = 1.4 kg2
= 
Note: In calculations like the above you should carry as many decimals as possible until the 
final result. The number of decimals to be retained at the end depends on the accuracy of the 
data values – one rule of thumb is to have one more decimal than in the original data.
Notice how the frequencies were used in the above calculation.
The calculator usage now has a small modification because we have been given the 
frequencies for the variable values. (There is no need to input each single observation.)
Graduate’s weight
(kg)FrequencyCumulative
frequency
6022
611416
62824
63125
64530
Σxi 2Σxi()2n⁄ –
n1 – ---------------------------------------
114 495 1 853()230 ⁄ –
29 --------------------------------------------------------114 495 114 453.6333–
29 ---------------------------------------------------------- 1 . 4 2 64==
xΣx
n------1853
30 ------------ 61.8 kg== 
						

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The keystrokes required are:
(press  to clear any data first)
 and the display should read 30
 and the display should read 61.766667
 and the display should read 1.1943353
 and the display should read 1.4264369
Thus, as expected
s = 1.2 kg, s2 = 1.4 kg2 and  = 61.8 kg
Exercise 6
Find the mean, standard deviation and variance of
(a) The annual rainfall data for the years 1971 – 1990
Ye a r1971197219731974197519761977197819791980
Rain 
(mm)1 3409901 1201 736 2601 1001 3791 1251 4301 446
Ye a r1981198219831984198519861987198819891990
Rain 
(mm)1 4591 6781 3459781 0021 1101 5461 6721 4671 123
x 
						

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(b) The sample of snail foot lengths
Answers:
(a) Rainfall statistics
mean:
µ = 1 265.3 mm
standard deviation:
 = 336.4 mm
variance:
σ2 = 113141.7 mm2
(b) Snail statistics
mean:
 = 3.4 cm
standard deviation:
s = 0.70 cm
variance:
s2 = 0.49 cm2
Snail foot length (cm)
2.24.13.54.53.23.73.02.6
3.41.63.13.33.83.14.73.7
2.54.33.43.62.93.33.93.1
3.33.13.74.43.24.11.93.4
4.73.83.22.63.93.04.23.5
σn-1
x 
						

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12. Trigonometric functions
The keys involved are:
Important: Make sure that your calculator is in the correct mode; mode 4 for calculations 
involving degrees and mode 5 for radians.
Example 1
In the right-angled triangle below, the length of the side opposite the 20° angle needs to be 
calculated.
To find the length of the side labelled x cm, use 
5 cm
20˚ x cm
tan 20
5
5tan20
x
x°=
⇒=° 
						

							30  Mastering the calculator using the Casiofx-82LB
The keystrokes on the calculator are:
 or 
The display should read 1.819851171, so the length of x is about 1.8 cm.
Example 2
In the right-angled triangle below, the length of the hypotenuse needs to be calculated.
To find the length of the side labelled x cm, use: 
The keystrokes on the calculator are:
The display should read 20.466631, so the length of the hypotenuse is about 20.5 cm.
Example 3
Given the lengths of two of the sides in the right-angled triangle below, find the value of the 
angle 
θ in degrees:
x cm
20˚ 7 cm
7sin 20
7
sin 20
x
x°=
⇒=
°
2 cm
1cm 
						

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In the diagram,  so 
To find the value of θ, you need to use the cos–1 key. The calculator keystrokes are:
Note: You must first get the value of the division by using the  key.
Your display should read 60°. If it does not, check that you are in degree mode.
13. Exponential and logarithmic functions
There are two log keys on your calculator, with their associated exponential keys. The latter 
are accessed by first using the shift key: 
The ‘log’ key uses base 10 and the ‘ln’ key uses base e (natural logarithm).
Example 1
Solve equation 
Taking logs of both sides;
1cos2θ=11cos ( )2θ−=
2a20= 
						

							32  Mastering the calculator using the Casiofx-82LB
To find the value of a, the keystrokes are:
The display should read 4.3219281.
So, . Confirm this by using the  key.
Example 2
Given , find the value of y
The  key is above the log key. Hence the keystrokes are:
The display should read 38.370725
Example 3 (harder)
Given , find the value of x
To  f i n d  l o g  x, the calculator keystrokes are:
The display should read 0.5187675.
Since this is the value of log x, you still need to find x where 
Without removing the answer of 0.5187675 on your display, press:
log 2 log 20
log 2 log 20
log 20
log 2
a
a
a=
⇒=
⇒=
4.32220≈yx
log y1.584 =
log y1.584 =
 
y⇒101.584=
10x
logx 61.5=
log 6 1.5
log 61.5log
log 6
log1.5
x
x
x
=
⇒=
⇒=
0.518767510 x= 
						

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Your display should now read 3.3019272
Note: You could use the ‘ln’ key instead of the ‘log’ key – the answer would still be the same. 
Try it!
14. Degrees, minutes, seconds
The key involved is 
This key can be used for problems involving degrees, minutes and seconds or hours, minutes 
and seconds. 
Example 1
Suppose that you have a trigonometric problem where the angle involved is given in degrees 
and minutes. e.g. Find x where 
’x4sin25° 36×= 
						

							34  Mastering the calculator using the Casiofx-82LB
The keystrokes involved are:
The display should show 1.728343, so x is approximately 1.73
Example 2
If you wish to convert an angle in degrees to its equivalent in degrees, minutes and seconds:
e.g. 34.88°, the keystrokes are:
The display should read 34°52°48, so the angle is 34°52’48’’.
Example 3
To find the sum of 5 hours 52 minutes 30 seconds and 7 hours 45 minutes 49 seconds:
The keystrokes are:
The display should read 13.638611 (hours).
To convert this number on the display into hours, minutes and seconds, press:
The display should now read 13°38°19 which is 13 hours 38 minutes and 19 seconds. 
						

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Review Calculator Exercises
1. Perform the following calculations
(i) (5 + 4) × 3
(ii) 12.5 – 8 ÷ 0.5
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
(ix)
(x)
(xi)
2. The following data is on growth (in $m) in an economy over a 8 year period:
2.5 6.2 -2.1 0.04 8.2 7.4 2.1 -1.7
Calculate (i) Σx(ii) Σx2(iii) (Σx)2 Explain in words what each of these mean.
368–×
4---------------------
12.8
1
6.5 3.8–------------------------
70.4117+×
47+ ()2 ×--------------------------------
2.4
3
4 -- - -
------
145.6 17.225⁄ –
345.6 17.22–5⁄
25327×
1.02 3
0---------------------+
4.1333 3.000– ()2.0150.1366
2
6 -------------------0.2000
2
6 -------------------+ ±
100 90– ()2
90----------------------------50 60– ()
2
60 -------------------------20 30– ()
2
30 -------------------------++