Ask Dr. Math

High School Archive

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

Selected answers to common questions:
    Mean, median, mode, range.
    Statistics glossaries.
    Weighted averages.

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Can An Event Be Statistically Impossible? [06/19/2007]

How small must the probability be for an event to be statistically impossible?

Central Limit Theorem [03/08/2002]

The probability that a drug is effective in any one patient is 62%. Find the probability that, of the next 200 patients, at least half (or more) will survive.

Chi-Squared Test for Independence [05/24/2000]

A hospital commissioned a study to see if there was a difference between the quality of care provided by hospital-trained and tertiary- trained nurses. How can I tell if the two events are independent?

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?

Class Intervals in Statistics [02/23/2009]

How can a class boundary be negative when all the data points are positive? Shouldn't the first interval start at 0 rather than -0.5?

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?

Confidence Intervals [07/24/2006]

A definition of confidence intervals and discussion of how they are sometimes incorrectly interpreted.

The Correlation Coefficient [09/11/1998]

How do you determine the correlation coefficient of a set of data, and its significance?

Correlation of a Scatterplot [02/04/1999]

Draw a scatterplot that represents no correlation, no positive correlation, and no negative correlation.

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.

Covariance [02/05/1997]

What does covariance represent?

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 Quartiles [07/20/2002]

I collected some data, and used several different programs to find the quartiles, but they gave different results! What's going on?

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?

Definition of a Rolling or Moving Average [03/05/2004]

When someone says they have calculated a "rolling average," what exactly does that mean? I cannot find the definition in any math books.

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...'?

Difference in Standard Deviation Formulas [01/31/2006]

When calculating a population standard deviation, why is (n-1) used in the denominator rather than n?

Distribution of Chi-square and F [12/03/2001]

Do chi-square and F have a mathematical relation?

Employee Turnover Rate [09/19/2002]

What is the formula to calculate employee turnover rate?

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?

Expectation and Hypothesis Testing [08/24/1999]

Four problems related to expectation and hypothesis testing in statistics.

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 a Formula That Fits the Data [01/26/2000]

How can I find a formula that fits a chart of tensile strength data I've collected?

Finding a Mean in a Survey [03/13/2002]

Question submitted via WWW:I have to figure out how to get a mean from a group of numbers after extracting a certain group of survey respondents...

Finding Line of Best Fit with Matrices [06/30/2004]

How can I find the line of best fit for a set of data using matrices?

Finding Outliers [09/28/2000]

How is the 1.5*IQR criterion used to find outliers in statistics?

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?

Finding the Next Number in a Sequence Given Its Geometric Mean ... Which Is a Square Root [09/24/2009]

A student who knows how to calculate geometric means gets rattled when trying to determine a sequence from its square root geometric mean.

Finding the Standard Deviation [8/5/1996]

What is the formula for calculating the standard deviation?

Find the Mode of a List [02/26/2001]

Is it possible to use other statistical measures to find the mode of a list of numbers, without knowing the numbers themselves?

The First Ace [06/12/1997]

An ordinary bridge deck of 52 cards is thoroughly shuffled. The cards are then dealt face up, one at a time, until an ace appears. What is the probability that the first ace appears at the kth card or sooner?

Frequency Table [10/13/2003]

What is a frequency table, and how do I make one?

General Comments on Standard Deviation [01/15/2004]

Answers to general questions about standard deviation including vocabulary, interpretation, calculation, and history.

Geometric and Arithmetic Means [5/10/1996]

Find two numbers whose sum is 20 and whose geometric and arithmetic mean is 8.

Graphing Scatter Plots [09/26/1998]

How do I make a scatter plot for height and shoe size? How can I make a graph online?

Grocery Store Statistics [06/10/1998]

Can you help me find confidence intervals and test for statistical difference on grocery store service time data?

How Do You Make a Circle Graph or Pie Chart? [12/16/2003]

I have some data on the weight of various parts of the human body. How do I turn that into a circle graph showing what percent of the total weight each part is?

How Many Samples? [03/30/1999]

For a continuous operation, how does one determine the necessary number of samples so that the mean of the samples represents the mean of the whole?

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