Calculating Mean & SD for Number of Cars per Household

  • Thread starter rowdy3
  • Start date
In summary: Weighted means is when you have a variable where the values can be in more than one category. So instead of just 1 to 5, like in the problem, you can have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Then the mean would be the total number of cars divided by the total number of weights. So in this problem, the mean would be 106/10 = 6.6.
  • #1
rowdy3
33
0
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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  • #2
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...
 
  • #3
The mean would be 3 and the sd be 1.6 ? Thanks
 
  • #4
If you're rounding, 3 is the mean. On the other hand, 1.6 seems a bit off.
 
  • #5
Sd comes out to 1.58.
 
  • #6
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.
 
  • #7
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?
 
  • #8
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.
 
  • #9
Thanks I got it now.
 

FAQ: Calculating Mean & SD for Number of Cars per Household

What is the purpose of calculating the mean and standard deviation for the number of cars per household?

The purpose of calculating the mean and standard deviation is to understand the average number of cars per household as well as the variation in this number across a population. This information can be used to make informed decisions or predictions about car ownership and usage.

How do you calculate the mean for the number of cars per household?

To calculate the mean, add up all the values for the number of cars per household and divide by the total number of households. For example, if there are 10 households with 1 car, 5 households with 2 cars, and 3 households with 3 cars, the calculation would be (10*1 + 5*2 + 3*3) / (10 + 5 + 3) = 1.23 cars per household on average.

How do you calculate the standard deviation for the number of cars per household?

To calculate the standard deviation, first calculate the mean as described above. Then, subtract the mean from each individual value for the number of cars per household, square these differences, and add them together. Divide this sum by the total number of households and take the square root. This will give you the standard deviation, which measures the spread of the data points around the mean.

Why is it important to calculate both the mean and standard deviation for the number of cars per household?

Calculating both the mean and standard deviation allows for a more complete understanding of the data. The mean gives a measure of central tendency, while the standard deviation gives a measure of the variation or spread of the data. Together, they provide a more accurate description of the data set.

Can the mean and standard deviation be affected by outliers in the data?

Yes, outliers in the data can significantly impact the mean and standard deviation. Outliers are data points that are significantly higher or lower than the rest of the data. In some cases, it may be necessary to remove outliers in order to get a more accurate representation of the mean and standard deviation for the number of cars per household.

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