Question

The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint.

3.4 2.5 4.7 2.5 3.6

2.8 3.1 5.6 3.4 2.8

4.3 4.2 5.1 3.1 4.7

Assume that the measurements are a simple random sample.

(a) What is the sample size for the above sample?

(b) Calculate the sample mean and the sample median for these data.

(c) Compute the sample variance and sample standard deviation.

Answer 1

• Sample Size
  Sample Size is the number of samples taken from a population to estimate the parameter of interest. Here, 15 samples are present. Hence, the sample size for this random sample is 15.
  
• Sample Mean
  The sample mean is given by:
  
  
  
  
  
• Sample Median
  The sample median is the middlemost observation of the ordered sample data.
  
  The ordered data from the above data is:
    2.5, 2.5, 2.8, 2.8, 3.1, 3.1, 3.4, 3.4, 3.6, 4.2, 4.3, 4.7, 4.7, 5.1, 5.6
  
  Thus the observation of the ordered sample data is the median.
  Now, the ordered sample observation is 3.4.
  
  Hence, the sample median is 3.4 .
  
• Sample Variance
  The sample variance is calculated as:
  
  
  
  
  
  
• Sample Standard Deviation
  The sample standard deviation is alculated as:
  
  
  
  
  
  
  

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