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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Standard Deviation for Variance? [01/25/2001]

I would like to calculate a measure of the reliability of my data. The best would be the standard deviation of variance. Does such measure exist?

Standard Deviation of Grouped Data [10/16/2000]

How do I find the standard deviation of grouped data in a frequency table? Also, how many significant digits should the mean of a data set have?

Standard Deviation of Sample [01/12/1998]

How can a given sample population have a narrower variance, hence a narrower standard deviation, than the entire population?

Standard Normal Random Variable [04/19/1999]

Find each of the following for a standard normal random variable Z...

Statistical Analysis - z and t Statistics [07/06/2004]

Could you tell me the differences between z-statistics and t-statistics?

Statistical Bias [09/27/2001]

Suppose that insted of choosing random samples of 25 students from a population of 100 students, you selected the first 25 students for the first sample, the next 25 students for the second sample, and so on. How might this sampling procedure bias the statistical results?

Statistics: Graphs and Pictograms [6/6/1996]

In statistics, what makes a graph a pictogram?

Statistics of Grouped Data [09/12/1999]

Can you show me how to find the mean, standard deviation, variance, and median class of grouped data?

Statistics - t-test [01/15/2002]

I am comparing scores of basketball games to see if playing at home is an advantage over playing away.

Stock Market Scam [02/08/2001]

Every Monday a firm sends you a letter correctly predicting the behavior of a given stock over the coming week. In the 8th letter the firm offers to sell you more predictions for a fee. You refuse. Why?

Stock Market Web Project [09/15/1997]

We are doing a pretend project on the stock market where we have $100 and have to invest in a stock. Do you have any tips or a good math activity for 6th grade students?

Student Grades [08/13/1997]

The grades of the students are normally distributed with a mean of 74 and a standard deviation of 10...

Taking a Weighted Average [03/20/2003]

I can't figure out the best way to get the average operating hours for the truck fleet.

Teaching the Concept of Average [06/20/2003]

How can I use blocks to teach averages to students?

Testing the Difference of Two Averages [05/27/1998]

I am given two averages, and I need to test whether they are statistically different.

T-Tests, P-Values, and Statistical Significance [03/18/2004]

I am doing a lab report comparing two different samples of fish. For the results the teacher wants a t test. What does the t value and two-tailed p value tell me and how do they compare to each other? Is this information 'significant' enough to say that variable 2 came from the same family as variable 1?

Types of Correlation [06/25/2002]

Can you explain positive, negative, strong, and weak correlation?

Understanding Standard Deviation [09/14/1998]

If two samples have different standard deviations, will the sample with the larger or smaller standard deviation show more variability?

Using a Computer to Make and Print a Scatterplot [11/23/2003]

Is there a way to use a computer to enter data and get a printout of a scatterplot so that I don't have to do it by hand?

Using Weighted Criteria to Make Decisions [07/18/2008]

I have three employees who have each worked different numbers of days and learned different numbers of skills in that time. How can I decide who is the most effective employee by weighting those two factors?

Using Z-Scores to Calculate Probability [05/25/2008]

Train cars are loaded with ore. The distribution of ore into the cars is normally distributed with a mean of 70 tons per car and a standard deviation of 0.9 tons. What is the probability that the weight of ore in a randomly selected car will be 70.7 tons or more?

Walking the Shortest Distance [10/07/2002]

A single boy lives in each of n equally spaced houses on a straight line. At what point should the boys meet so that the sum of the distances that they walk from their houses is as small as possible?

Weighted Coin Project [02/01/1997]

Analyze the results from flipping a non-weighted coin and a weighted coin.

What Does Average Mean? [12/05/2001]

Can someone explain what average is? For example what is the average rainfall in New York? I understand the formula needed to find the average, but what is the meaning of average?

What Does the Median Order Value Mean? [05/17/2010]

A business struggles to describe its sales performance with an appropriate measure of central tendency. Doctor Wilko clarifies, using scenarios in which medians remain unchanged while average sales change -- or the two move in opposite directions.

What Field Studies Small Groups with a Characteristic? [6/10/1996]

What field studies questions like: 1. Take for example that person A has blonde hair. 2. You know that this person is not famous. 3. You also know that (10) people know person A. 4. You would like to know that if (10) people know person A, how many people in a given population also know someone like person A, someone with blonde hair. 5. You really want to know how many people with blonde hair there are in a given population given the answer to #4.

What is a Median? [03/03/1998]

A definition of median, and four examples of calculating medians.

What is the Meaning of "Average"? [03/28/2007]

An interesting conversation that defines the general concepts of average and central tendency, and looks at the usefulness of such measures both in representing the data and for making predictions about future events.

What is the Regression Line? [08/09/1999]

Determining the line that is as close as possible to passing through all the points on a scatterplot.

Which is the Best Description? [03/25/2001]

Which best describes the number of times "Popular Song" was played on the radio per day: the range, the median, the mode, or the mean?

Which Measure of Average is the Best to Use? [08/17/2006]

I have collected over 120 observations of Internet connection speeds through my current provider. What is the best way to find an average of those speeds so I can convince the provider that the service is slow?

Why Do We Calculate Standard Deviation the Way We Do? [02/05/2004]

Why do we square the deviations and then take the square root when calculating standard deviation? Why can't we just take the absolute value of the deviations?

Why Is the Least Squares Line the Best Choice? [11/03/2005]

When looking for a prediction line for the relationship between two variables, one method is to find the least-squares line. What about the least squares line makes it the best fit for the data?

Why Learn about Probability and Statistics? [04/17/2002]

Why is probability so important to learn? When will we use it in the real world?

Why Take Averages in Experiments? [05/04/2003]

I have to measure the time it takes from when I release a toy car until it reaches the bottom of a 6-foot ramp.

Winning the Lottery [01/30/1997]

Can you find a formula that predicts the outcome of the lottery?

Zero Correlation Does Not Imply Independence [11/04/2003]

Can you provide an example of random variables that are not independent, but have a correlation of zero?

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