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Browse Middle School Statistics
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Graphs: bar graph, histogram, pictogram.
    Mean, median, mode, range.
    Statistics glossaries.
    Weighted averages.

Calculating Average Starting Time [06/23/2003]
How do you average a series of starting times to get the average starting time? Say 9:30a.m., 10:15a.m., 11:45a.m., 1:30p.m., and 11:30a.m.

Finding the Next Number in a Sequence
Given Its Geometric Mean ... Which Is a Square Root
A student who knows how to calculate geometric means gets rattled when trying to determine a sequence from its square root geometric mean.

Grade and Test Averages [12/02/2001]
In a class of 21 students the average score on a math test was 77%. If Suzie got 95% and Jack got 78%, find the average grade of the other 19 students.

Mean, Median, Mode, Range [11/23/1997]
What are the definitions of mean, median, mode, and range?

Stem and Leaf and Scatter Plots [10/13/1998]
Information on stem and leaf plots and scatter plots.

Add Up Data First, Then Take the Average? Or Take the Averages First, Then Add? [01/20/2010]
Doctor Peterson explains weighted averages, using an extreme example to illustrate how the order of operations that you choose will emphasize different qualities of the same data set.

Arithmetic vs. Geometric Mean [03/27/2001]
When is it appropriate to use the arithmetic mean, and when the geometric mean?

Average [05/10/2001]
Is it true that the average of a set of data is always computed by adding all the numbers together and dividing by the total number?

Average Racing, and Faster Averaging [08/27/2015]
A teen struggles to determine the sixth data point to add to a set of five in order to achieve a target mean. Stepping through several similar examples, Doctor Ian models the procedure   and introduces offsets as a shortcut.

Average Speed and How It Relates to Average in General [10/07/2008]
The average speed of an object is found by dividing distance by time. A basic numeric average is found by adding up the numbers in the set and dividing by how many there are. How does this basic average relate to average speed, or are they unrelated?

Average Wind Direction [05/21/1997]
Given a weather instrument that records wind direction, determine the average wind direction.

Averaging Ages [11/17/1999]
What is the average age of these 4 children...

Averaging Kelly's Test Scores [01/07/2002]
Kelly's average score on 4 tests is 85.5. The average of her 3 highest scores is 87, and her two lowest scores are the same as each other. What is the average of her two highest test scores?

Averaging Percentages [12/11/1998]
Why can you average percents in the usual way in some cases, and why do you have to use weighted averages in others?

Bar Graphs and Histograms [04/30/2008]
What is the difference between a bar graph and a histogram? What are the similarities? Which graph explains more details?

Bar Graphs vs. Histograms [09/05/2002]
What is the difference between bar graphs and histograms?

Biased and Unbiased Surveys [11/05/2008]
The Tri-State Soccer League is conducting a survey to determine if the players want to change the style of soccer shirt. If they randomly survey all players who wear size large shirts, is the survey biased or unbiased? I'm not sure what those two words mean.

Binomial Experiments [09/05/2003]
How can I explain the binomial distribution to my six grade math class?

Box and Whisker Plots [02/13/2000]
Can you explain how to make and use box and whisker plots?

Box and Whisker Plots [05/18/2000]
If there is an odd number of points in a data set, is the median considered to be part of the subgroup used to find the upper (or lower) quartile?

Breaking the Mode [12/23/2016]
Grouped data giving you more than one mode? Make better choices about your classes and their widths.

Calculating a Grade Average [08/15/1999]
How can I figure out my average if some things are worth more than others?

Calculating a Weighted Average Grade [05/05/2000]
What is the grade if the following make up the final grade: 45% = 3 tests (85, 78, 92), 25% = final (94), 15% = project (91.9), 15% = 3 case questions each worth 25 points (25, 25, 23.5)?

Calculating Percentage of Errors [03/21/2002]
You have items to be picked off a shelf every day. You pick one item a day and check it against the order. You wish to asign a percentage to the error in wrong items and/or number of items.

Can An Event Be Statistically Impossible? [06/19/2007]
How small must the probability be for an event to be statistically impossible?

Choosing between Median and Mode as the Best Representation [03/02/2009]
A set of data contains the numbers 1, 3, 9, 10, 13, 15, 25, 39, 58, 63. Which measure of central tendency best represents the data?

A Closer Look at the Definition of Median [08/14/2008]
If you have five numbers like 100, 200, 300, 400, 500, the median or middle number is 300. How does this divide the set of numbers into two equal groups?

Counting Techniques [12/29/1997]
Find the number of positive divisors of 17640, inclusive of 1 and 17640 itself. Find the number of odd integers between 2000 and 7000 that do not have repeated digits.

Data Set With Specified Mean, Median, Range [12/11/2003]
Make up a set of 5 numbers with a mean of 20, a median of 10, and a range of 50.

Defending the Mean [09/07/2003]
I know how to find the mean of a set of values, but can you explain why it's defined the way it is?

Defining Relative Error [03/11/2004]
I've seen "relative error" defined both as "the absolute error divided by the true measurement" and "the greatest possible error divided by the measurement itself." These definitions seem to be inconsistent. Which one is correct?

Definitions: Average, Mean, Mode [5/20/1996]
Arithmetic, geometric, harmonic means defined.

Definitions of Range [10/20/2003]
I can find only one definition of range in the math dictionaries - the difference between the smallest and the largest number in a set. We are always talking about 'They range in age from, or they range in height, or they range in weight, or they range in size, etc'. If the only defintion of range is the difference, why do we say 'They range...'?

Examples of Weighted Averages [03/26/2001]
Can you tell me what is meant by "weighted average," and give me some examples of when and how weighted averages are used?

Explaining Independent and Dependent Variables [10/25/2002]
Can you elaborate on the definitions of independent and dependent variables?

Explaining Weighted Averages [09/24/2002]
Can you please give me a layperson's explanation of why and how to use a weighted average?

Finding an Average without the Individual Numbers [09/12/2006]
A total of 50 juniors and seniors took a math test. The 35 juniors had an average score of 80 while the 15 seniors had an average score of 70. What was the average score of all 50 students who took the test?

Finding Average Times [02/15/2002]
My son and I have started a physical fitness program, and we are keeping track of our time for the mile. At the end of the week we would like to figure our average time.

Finding Mean, Median, Mode [03/29/1998]
Can you show me how to find the mean, median, mode, and range of a set of scores?

Finding the Median with Ties [06/16/2009]
The median of the set {2,3,5,5,5,10} would be 5, but that leaves one value greater than the median (10), and two values less than the median (2 and 3). So how can 5 be a measure of central tendency, and is there a different way to calculate the median in this case?

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