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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Hypothesis Testing [04/22/1999]

Why when the p-value is lower does the null hypothesis value fall more easily in the 95% confidence interval?

Ice Skating Scoring [01/27/2001]

Why does the U.S. Figure Skating Championship use only five scores out of the seven given by judges?

The Idea behind z-scores, and Their Relation to Standard Deviation [06/24/2010]

A student familiar with the definition of z-scores wonders why we use standard deviations to calculate them. Illustrating two ways, Doctor Peterson explains the concept of scaling that motivates this statistical measure.

Independence of Mean and Variance of a Sample [12/14/2008]

If a random sample is taken from a normal distribution, the mean and variance of that sample are independent. Further, this independence is only true for normal distributions. I don't understand how they can be independent when they are from the same sample values.

Interpolation Polynomials and Linear Regression [10/09/1998]

I need to find the polynomial of a temperature curve using some data I have gathered.

Interpreting a Correlation [08/06/2004]

Does a correlation of 0.60 between teacher attire and student academic performance indicate that encouraging teachers to be properly attired will increase academic performance?

Interpreting Chi-Squared Test Results [10/26/2004]

The critical values for chi-squared increase as the confidence level increases. My question is why does a distribution "pass" this test if the calculated value is less than the critical value and not vice-versa?

Interpreting Coefficients of Correlation [07/01/2004]

Given a coefficient of correlation of r = 0.66, state what percent of variation in y is due to the variation in x.

Interpreting Stemplots [05/11/1998]

What does a stemplot represent, and how does it relate to the overall population?

Interquartile Range and Standard Deviation [11/24/1997]

What are some uses of interquartile range and standard deviation?

An Introduction to Exponential Growth [10/07/2006]

What exactly is exponential growth? I see an equation in my book, but I'm not sure what it means or how it works.

IQ Scores by Category [7/28/1996]

Suppose an IQ test is given to a large group of people. Find the percent of people whose IQ scores fall into the following categories...

IQ Tests and Standard Deviation [7/28/1996]

On standard IQ tests, the mean is 100, with a standard deviation of 15. Find the percent of people whose IQ scores are greater than 115...

Is There a Mode when All Data Points Occur Equally? [05/02/2007]

If you have a set of data such as {2, 15, 20, 39, 56, 67} is there a mode, and if so, what would it be?

Lagrange Interpolation [08/20/2003]

I am trying to learn Lagrange interpolation.

Large Standard Deviations [12/24/1997]

Is there a way to calculate the percent values derived from the z-table without using the table, i.e. a formula?

The Law of Large Numbers [02/08/2001]

Can you give me a brief explanation of the law of large numbers?

Lifespan Probability [03/26/1999]

The probability that a general population will live past 85 is estimated to be 5.4 percent...

Line of Best Fit Using Least Squares Method [06/08/2005]

Can you give me a basic explanation of the math behind the method of finding the line of best fit using the least squares regression?

Local Modes and Bimodal Distributions [10/22/2000]

What does it mean if a frequency distribution shows two peaks?

Manipulated and Responding Variables [01/13/2002]

What are manipulated variables and responding variables?

Mean and Standard Deviation [03/01/1999]

Prove that the mean (u) and standard deviation (s) for a binomial distribution are np and the square root of (npq).

Mean, Average, and Standard Deviation [04/18/2001]

Why is the average of means of three groups not always equal to the mean of the three groups put together?

Mean Less Than Median [08/17/2003]

Can you draw any valid conclusions about a set of data in which the mean is less than the median?

Mean, Median, and Mode [07/15/1998]

Can you explain the three ways to represent a group - mean, median, and mode? I am having trouble understanding the mode.

Mean, Median, and Mode in Real Life [12/21/1996]

What are some real life examples involving mean, median, and mode?

Mean, Median, Mode: Find Five Numbers [05/10/2001]

The median of five numbers is 15. The mode is 6. The mean is 12. What are the five numbers?

Mean or Median? [11/02/2003]

How do you decide whether to use the mean or the median to describe a set of data? Why would one be higher or lower than the other?

Median and Middle [5/15/1996]

I would like to know how to find the median of two of the same numbers (2 and 2).

Mode, Mean, and Median in Stemplots [02/21/2002]

How do I find a mode, mean, and median, using a stem/leaf plot?

Mode of a Uniform Distribution [09/06/2000]

What is the mode of a set of numbers, if none of the numbers repeat themselves? What about a set like {1,1,2,2,3,3}?

More Living or Dead? [08/14/1997]

Are there more people living now than have ever died?

More Than One Mode? [10/07/2002]

Can a data set have more than one mode?

New Pension Plan [07/15/1999]

Is there an relation between age and an employee's opinion of the new plan?

Normal Distribution [6/24/1996]

In six successive independent 'triple jumps' what is the probability that at least one total distance will exceed 18 meters?

Normal Distribution Curve [11/13/2000]

What is the normal distribution curve?

Null Hypothesis, Deviation [08/05/1997]

A statistician believes that on the average the members of a group of people weigh 120 pounds...

One Chicken, One Day [04/19/2002]

If a chicken and a half lays an egg and a half in a day and a half, how many eggs can one chicken lay in one day?

One Tailed, Two Tailed t-Tests [09/11/1998]

What is the difference between a one-tailed and two-tailed t test?

Ordering Probabilities [08/13/1997]

The proportion of people who order coffee with their dinner is .9. A simple random sample of 144 patrons of a restaurant is taken...

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