Statistics; Mean; Variance - HP 3456A Operating And Service Manual

Operation
to the ohms function. It is advisable to first select an
ohms range which corresponds closely to the resistance
value of the thermistor for the temperature to be
measured. When the Thermistor operation is selected.
the ohms reading (thermistor resistance) is then
calculated by the instrument and can be displayed either
in degrees C or degrees F dependent on which math
feature is selected. The Thermistor math operation with
the results displayed in degrees C is selected by the "6"
(0C) key. The "5" (OF) key is used for degrees F. Refer
to Table 1-1 for the Thermistor accuracy specifications.
The recommended Thermistor can be ordered by -hp
Part Number 0837-0164. A package of 4 thermistors is
also available under Accessory Number 44414A. The
thermistor's corresponding resistor value at high and
low temperature limits
temperature is:
Temperature
150°C
25°C
-80°C
3-95. Keep a couple of things in mind when using the
Thermistor mode. Choosing an optimum ohms range
for the termperature measurement has been mentioned
in the preceding paragraph. This is important for a
stable reading. You can use other ranges or autorange.
but the reading may be unstable. To demonstrate this,
choose a high ohms range for the thennistor. An ohms
reading is still taken and the temperature is still
calculated; but since a higher range is more sensitive for
low ohms values. the reading is not as stable. Autorange
may have the same effects, since there may be a dif­
ference from range to range. Another thing to keep in
mind is lead resistance. If 2-Wire Ohms is used, any lead
resistance is added to the thermistor resistance causing
an inaccurate temperature reading.

3-96. Statistics.

3-97. The Statistics math feature of the -hp- Model
3456A is used to make a Mean and Variance calculation
of reading(s) taken in any function. These calculations
are made when the instrument is set to the Statistics
(ST AT) mode and after a measurement cycle is com­
pleted. The Mean value is then stored into the MEAN
register with the number of readings taken stored into
the COUNT register. The Variance value is stored into
the VARIANCE register with highest reading taken
stored into the UPPER register and the lowest reading
into the LOWER register. In addition, the first reading
taken is also stored into register Z. Except for the
Variance calculation, all other statistics calculations are
done after the first measurement cycle is completed. The
Variance calculation needs at least two readings to
calculate its value. The default values of the MEAN,
VARIANCE, COUNT, UPPER, LOWER, and Z
registers are 199999 +9, - 00.000 - 3 CO), 0, 1999999
+9, - 1999999 + 9 , and 0 respecitvely. The Statistic
3-16
and at nominal room
Resistance
92.7 Ohms
5000 Ohms
3684 K Ohms
mode is selected by the "2" (STAT) key. To reset the
registers to their default values without pressing the
3456A's RESET button or cycling power, select the
statistics function again by pressing the MATH button
and STAT key. Refer to Table 1-1 for the Statistics Ac­
curacy Specifications.
NOTE
Since the math calculations are made to
digits, certain accuracy limitations
in Table 1-1 should be kept in mind.
The Mean (Average) value is calculated by

Mean_

3-98.
the formula:
+
Mean (M) = X I
C
Where "X i is the "ith" reading taken after enabling
statistics, "Xl" is the first reading taken after enabling
Statistics, and" C" is the total number of readings taken
with the present reading (X) displayed on the front
panel. The present Mean value is in the MEAN register
and it, along with the other registers used in the
Statistics mode, can be recalled. at any time by recalling
the appropriate register.
The Variance value is calculated by the

Variance.

3-99.
formula:
Variance (V)
=
C
E
(X. - X) ' -
i I
I
=
C - 1
Where "Xi" is the "ith" reading taken after enabling
statistics, "X I " is the first reading taken after enabling
Statistics and " C" is the total number of readings taken
with the present reading (X) displayed on the front
panel. The present Variance value is in the VARIANCE
register and it, along with the value(s) in the other
register{s), can be recalled at any time by recalling the
appropriate register.
Statistics Example.
3-100.
feature is to calculate the average value of a number of
resistors. Start by setting the 3456A to the ohms func­
tion and Single Trigger mode. Then select the Statistics
Math mode. Next connect the first resistor to the input
terminals and trigger the instrument (push the SINGLE
trigger button). Do the same for the other resistors after
the measurement cycle is completed. When all of the
resistors are measured, you can determine the average
value of the resistors by recalling the MEAN register.
The Variance of the register values can be recalled by
the VARIANCE register. To doublecheck the number
of resistors you have measured, recall the COUNT
Model 3456A
9
shown
as
C
I
1:
(X i - XI) = X
= 1
C
,
E
-'-
C i
= 1
One way to use the Statistics
)
J