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52 West Main Street
Washingtonville, NY 10992

Phone: 845.497.4000
Fax: 845.497.4030

How do you get to Carnegie Hall? Practice. Practice. Practice.

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Topic of the Week: 

Quartiles
and
Interquartile Range
Mr.Chin's Class:  Prepare to take your Quarterly 4 on Friday, June 15th.
Mr. Andersen's ClassPrepare to take your Math Quarterly 4 on Thursday, June 14th.
Skeleton Notes
A.  Statistical Measures
Mean - the average; add and then divide by the number of datum
Median - middle score; if you divide your data list in half, it's the middle score; if there are two middle scores, then calculate the mean of those two - that will be your median
Mode - most commonly occurring piece of data (number)
Range - the difference between the highest and lowest score
 
B.  Data comes in two different forms
1. categorical data - names and labels
2. numerical data - numbers or amounts 
 
C.  Dot Plots - A type of graph that uses dots to keep track of each piece of data. A dot is placed above each number in a straight line.
 
D. Intervals - ranges of numbers; histograms use groupings so that they can include ranges of numbers in small groups; it allows the user to keep track of large amounts of data; the traide off is that we are not able to see exact points of data. 
 
E. Frequency Tables and Relative Frequency Tables
Frequency tables help us to see actual numbers of specific data in specific amounts. It uses tally marks and totals. The higher the frequency, the more often the specific number happens.
Relative Frequency tables are the same as the frequency tables, in that they measure frequency using tally marks. There is an added column in which the frequency is divided by the total number of data (tally marks) which gives a decimal or percentage of the frequency of each particular piece of data happening. 
 
F. Quartiles
Quartiles are the values that divide a group of numerical data into four equal parts (quarters).
To find the quartiles, follow these four simple steps.
1. Write your data into numerical order (from least to greatest).
2. Determine the median - identify it or calculate it. This should break your list into two equally sized groups of data. This is your second quartile (Q2)
3. Determine the middle value of the lower group of data. This is your first quartile (Q1).
4. Determine the middle value of the upper group of data. This is your third quartile (Q3).
 
G. Interquartile Range
The interquartile range or IQR measures the difference between the Q1 and the Q3 of a set of numerical data. It is found by subtracting the Q1 from the Q3.  
Using the formula below may help you to get consistent results. You will still need to find the Q1 and Q3 before using it.
Q3 - Q1 = IQR
H. Comparing Measures of Central Tendency
When we compare measures of central tendency, we might compare the mean of a set of data to the median.  It could also be comparing the mode to the range.  Any of these comparisons may include any of the four (mean, median, mode and range).
 
I. Mean Absolute Deviation
Mean Absolute Deviation is also known in our class as the M.A.D.  It is the mean or average distance (or difference) of each piece of data from the actual mean of the data.
1. Calculate the mean.
2. Subtract each number from the mean or subtract the mean from the number. Find the difference.  
3. Calculate the average of these differences. This will be your M.A.D.
 
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52 West Main Street Washingtonville, NY 10992  |  Phone: 845.497.4000  |  Fax: 845.497.4030
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