Download Quick Summary: Highlights of Sections 9.1 and 9.2

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 to be the average of the two middle numbers (in
value).]
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 variance or standard deviation by hand. However, in practice, you
will want to use the computer calculator that will be available to you in the math lab for your test. This is the
Windows 7 calculator…the one you must use on tests. (Calculators under other versions are different.)
Directions for using the Windows 7 calculator to calculate the standard deviation (mean) of a set of numbers:
1. Make sure that the calculator is in 'Statistics' mode. (The modes are on the View Menu.)
2. Enter the first number from the dataset and click 'Add' at the lower right.
(Clicking the 'Add' button puts the number into the 'Statistics Box'.)
3. Enter the remaining numbers in the dataset, clicking 'Add' after each one.
Hint: Use copy/paste when you need to enter the same number multiple times.
(You can see the numbers in the 'Statistics Box' along with a count of how many numbers were entered.)
4. Once all of the numbers have been entered (and double-checked), click the ' σn-1 ' button
(just above 'Add') and the standard deviation, s, will appear in the main calculator window.
(Click ' ' instead of ' σn-1 ' if you want the mean instead of the standard deviation.)
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) Steps:
1. Find the midpoint of each interval (xmp)
2. Multiply each midpoint by its frequency (f)
3. Add up all the resulting products
4. Divide this sum by n (which is just the sum of the f ’s)
Calculating a GROUPED VARIANCE / STANDARD DEVIATION (by hand) Steps:
1. Calculate the square of each midpoint
2. Multiply each square by its frequency
3. Add up these products
4. Plug into the formula to the right (s2)
5. Take the square root to get s (if you want s instead of s2)
The formulas above allow you to calculate the mean, variance or standard deviation of grouped data
by hand. However, in practice, you will want to use the computer calculator that will be available to
you in the math lab for your test. This is the Windows 7 calculator…others are different).
Directions for using the Windows7 calculator to calculate the mean, standard deviation, or
variance for grouped data:
1. Find the midpoint of each interval. (Add the endpoints and divide by two.)
2. Make sure that the calculator is in 'Statistics' mode. (The modes are on the View Menu.)
3. Enter the first midpoint calculated in step 1 and click 'Add' at the lower right.
(Clicking the 'Add' button puts the number into the 'Statistics Box'.)
4. Enter the remaining midpoints calculated in step 1, clicking 'Add' after each one.
(You can see the numbers in the 'Statistics Box' along with a count of how many numbers were entered.)
5. Once all of the numbers have been entered (and double-checked), click the ' σn-1 ' button
(just above 'Add') and the standard deviation, s, will appear in the main calculator window.
(Click ' ' instead of ' σn-1 ' if you want the mean instead of std deviation & square the ' σn-1 ' if you want variance.)