Calculating Mean & SD for Number of Cars per Household

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Discussion Overview

The discussion revolves around calculating the mean and standard deviation for a frequency distribution of the number of cars per household based on a random sample of 530 households. Participants explore the correct methodology for these calculations, including the implications of using frequency data.

Discussion Character

  • Homework-related
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant presents a frequency distribution and claims to have calculated a mean of 106 and a standard deviation of 48.13 using a calculator.
  • Another participant questions the validity of the mean of 106, suggesting it does not make sense in the context of the problem.
  • Some participants propose that the mean should be 3 and the standard deviation 1.6, but this is met with skepticism regarding the standard deviation value.
  • One participant provides a corrected standard deviation of 1.58, indicating a possible error in earlier calculations.
  • Another participant encourages posting the steps taken to solve the problem to identify errors in reasoning.
  • A hint is provided about looking up weighted means, suggesting that the calculations should consider the frequency of each category.
  • A later reply indicates that one participant has resolved their confusion regarding the calculations.

Areas of Agreement / Disagreement

Participants express disagreement regarding the calculated mean and standard deviation, with no consensus reached on the correct values or methods to use. Some participants believe the mean should be 3, while others challenge this conclusion.

Contextual Notes

There are unresolved issues regarding the methodology for calculating the mean and standard deviation from frequency data, including the potential need for weighted means. The discussion reflects varying levels of understanding and interpretation of the problem.

Who May Find This Useful

This discussion may be useful for students learning about statistical calculations, particularly in the context of frequency distributions and weighted means.

rowdy3
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A random sample of 530 households resulted in the following frequency distribution for a number of cars per household. Find the mean and standard deviation.
Number of cars ¦ Frequency
1 ¦ 61
2 ¦ 108
3 ¦ 179
4 ¦ 118
5 ¦ 64
Sorry don't know how to put this in a box. Under cars it's 1,2,3,4,5. Under frequency it'a 61,108,179,118,64. I typed the Freq. into my calculator and my mean was 106 and my standard deviation was 48.13.
I was marked off 6 points. Shoud I have just done cars? Put that into my calculator and my mean would be 3 and my sd be 1.6?
Thanks
 
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Try re-reading the problem then try to understand the question. It's asking you to find the mean number of cars, right? Your answer was 106. Does that make sense? Do you really think the mean number of cars per household is 106? I wish I had that many cars...
 
The mean would be 3 and the sd be 1.6 ? Thanks
 
If you're rounding, 3 is the mean. On the other hand, 1.6 seems a bit off.
 
Sd comes out to 1.58.
 
You should post the steps you are taking to solve the problem. That way we can see where you are making an error and correct it.
 
Oh god, I just realized how you're coming up with mean = 3 and stdev = 1.6...

Re-read the question, and again try to understand the question. After you've done that, answer this: what is the total number of cars?
 
rowdy3 said:
A random sample of 530 households resulted in the following frequency distribution for a number of cars per household. Find the mean and standard deviation.
Number of cars ¦ Frequency
1 ¦ 61
2 ¦ 108
3 ¦ 179
4 ¦ 118
5 ¦ 64
Sorry don't know how to put this in a box. Under cars it's 1,2,3,4,5. Under frequency it'a 61,108,179,118,64. I typed the Freq. into my calculator and my mean was 106 and my standard deviation was 48.13.
I was marked off 6 points. Shoud I have just done cars? Put that into my calculator and my mean would be 3 and my sd be 1.6?
Thanks

Hint: Look up weighted means (of an ordered categorical variable). That's all I'm going to say. If you come back, someone else may help you.
 
Thanks I got it now.
 

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