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=...

Mastering the calculator using the Casiofx-82LB  27
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...

28  Mastering the calculator using the Casiofx-82LB
(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 

Mastering the calculator using the Casiofx-82LB  29
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...

Mastering the calculator using the Casiofx-82LB  31
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...

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...

Mastering the calculator using the Casiofx-82LB  33
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...

Mastering the calculator using the Casiofx-82LB  35
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...