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Below are some sample problems. While they are relatively simple, they only serve as an illustration of a few concepts offered as pointers, free of charge. For specific math or statistics help with your math/statistics online class, please feel free to contact us for a quote. Be it the statistical analysis you’ve been dreading for your graduate research project, or a few simple problems from your entry-levels statistics course, our experts can handle it! So, go ahead and give us a shot, we guarantee you will not be disappointed! We offer the statistics help you need to succeed!

Standard Error of a mean

Q:        A certain soft-drinks manufacturer found that the standard deviation in the weight of soda-filled cans coming off the production line is 0.006lb. It is company policy to calculate descriptive statistics for the mass (and other attributes) of samples comprising 36 filled cans. The mean weight for one such sample was found to be 0.817lb. What is the error associated with that value?
A:        If we were to draw 36-can samples from the population of all the cans filled at the factory, the sample means would be normally distributed, regardless of the population distribution. However, if we were to compare the deviation between the population mean and all the means from hundreds of 36-can samples, that standard deviation would be the same as that between the different sample means. This relationship gives rise to the formula below:

stats image
           
where StDev is the population standard deviation, n is the sample size.
For our example, stats2 


Standard deviation for frequency distributions
Q:        A sample of 50 6th grade students was asked to take an IQ test, and their scores are shown in the frequency distribution below. Calculate the standard deviation of their IQ scores.


IQ Score

71-79

80-88

89-97

98-106

107-115

116-124

125-133

Frequency

2

8

10

12

6

8

4

A:        Since we are given frequency classes, we must first find the mid-point of each class in order to calculate the standard deviation. Additionally, the formula we will use must take into account the frequencies for each midpoint value based on the class frequencies above. That formula is:    statistics example where f is the frequency and x is each midpoint value
The midpoint values are stats 3 as shown in the table below. The mean is calculated from the midpoints and their respective frequencies; stats help3 


x

75

84

93

102

111

120

129

stats 4 help

748.5696

337.0896

87.6096

0.1296

74.6496

311.1696

709.6896

statistics help 4

1497.139

2696.717

876.096

1.5552

447.8976

2489.357

2838.758

statistics example

216.9504

statistics help 5

14.72924

 

As shown above, the standard deviation in IQ scores is 14.73
Remember that standard deviation is a measure of variability, however with frequency distributions since information has already been “lost” when grouping individual data points in frequency intervals, the standard deviation from such  a distribution should not be compared to that of a population where all the individual data-points are known (and used to calculate the standard deviation).


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