Download Section 9.1 and 9.2 Summary

Quick Summary: Highlights of Sections 9.1 and 9.2
Measures of Central Tendency
The MODE is defined to be the most frequent number in a set of numbers.
The MEDIAN is defined to be the middle number (in value) in a set of numbers.
[If there is no 'single' middle number (in value), the median is defined as the average of those 2 middle
numbers.]
The MEAN is defined to be the ordinary arithmetic average of a set of numbers.
[Sum the numbers and divide by the number of numbers in the set.]
Measures of Variation
The SAMPLE RANGE is defined to be the Largest Value - Smallest Value in the sample.
The SAMPLE VARIANCE (s2) is defined as:
The SAMPLE STANDARD DEVIATION (s) is defined to be the square root of the Sample Variance:
Shortcut formula for calculating the SAMPLE VARIANCE/STANDARD DEVIATION (by hand)
The formula above lets you to calculate the mean or standard deviation by hand. In practice,
you will want to use your own calculator (one allowed in the MTLC for your test). Below is
how this calculation is done on the CASIO fx-260 calculator. (Other calculators will be at least
somewhat different.)
Detailed instructions below show how to use the CASIO fx-260 calculator to do these
calculations.
Working with GROUPED DATA
Range of scores (x interval)
12 - 17
18 - 23
24 - 29
30 - 35
Example of a FREQUENCY DISTRIBUTION
Frequency (f)
3
6
4
2
Example of a FREQUENCY HISTOGRAM
Calculating a GROUPED MEAN
BY HAND
USING THE CASIO fx—260 CALCULATOR
1. Find the midpoint of each interval (xmp)
1. Find the midpoint of each interval (xmp)
2. Multiply each midpoint by its frequency (f)
2. Enter each midpoint into the Stats Mode
3. Add up all the resulting products
of the calculator & then press
4. Divide this sum by n
(which is just the sum of the f ’s)
SEE THE ‘STATS ON THE CASIO fx-260’
SHEET FOR MORE DETAILED INSTRUCTIONS.
Calculating a GROUPED VARIANCE/STANDARD DEVIATION
BY HAND
USING THE CASIO fx—260 CALCULATOR
1. Calculate the square of each midpoint
1. Find the midpoint of each interval (xmp)
2. Multiply each square by its frequency
2. Enter each midpoint into the Stats Mode
3. Add up these products
of the calculator & then press
4. Plug into the formula for s2
5. Take the square root to get s
(if you want s instead of s2)
SEE THE ‘STATS ON THE CASIO fx-260’
SHEET FOR MORE DETAILED INSTRUCTIONS.
The procedure above shows you how to calculate a group mean or standard deviation by hand. In practice, you
will want to use your own calculator (one allowed in the MTLC for your test). Below is how this calculation is
done on the CASIO fx-260 calculator. (Other calculators will be at least somewhat different.)
Instructions below show how to use the CASIO fx-260 calculator to do these calculations.
Chebyshev’s Theorem: For any set of numbers, a fraction of at least
of them will be within K standard deviations of the mean.
So, for example, for k=2 standard deviations of the mean, at least
of the numbers in the data set will be within 2 standard deviations of the mean.
STATS on the CASIO
fx-260 SOLAR
Calculator
Wakes up the calculator…but it also clears out any
old data previously stored.
Puts calculator into Stats (SD) mode [indicated by
‘SD’ in upper right of display].
Clears old stats data (but unlike the ON button, it
leaves you in Stat mode)
Key in a number & press M+ to add it to the dataset.
Once your dataset has been entered, this calculates
the mean.
Once your dataset has been entered, this calculates
the (sample) standard deviation.
Note: Once a number is entered, pressing
enters it again.
Shortcut to enter the same number multiple times:
7x8
automatically enters the number 7 eight times
(the long way: 7
7
7
7
7
7
7
7 )
Note: If you enter a number in error, you can take it out by re-entering
the number and pressing SHIFT
.
Note: You can use SHIFT to display how many numbers have been
entered so far.