Question

In: Statistics and Probability

The marketing team at an internet music site wants a better understanding of who their customers...

The marketing team at an internet music site wants a better understanding of who their customers are. They send out a survey to 25 customers​ (and use an incentive of​ $50 worth of downloads to guarantee a high response​ rate) asking for demographic information. One of the variables is the​ customer's age. For the 25​ customers, the ages are shown to the below. Complete parts​ a) through​ d).

19 , 30 , 39 , 26 , 36 , 32 , 31 , 22 , 23 , 43 , 35 , 13 , 44 , 31 , 44 , 29 , 28 , 47 , 36, 44 , 31 , 12 , 27 , 33 , 47

a)Find the quartiles Q1 & Q2

​b)Find the quartiles Q1 & Q2 using the Tukey method.

​c)Find the IQR using the quartiles from part b.

d)Find the standard deviation.

Solutions

Expert Solution

Solution: a) Find the quartiles Q1 & Q2

Solution: First we need to sort the data in ascending order:

  

  

  

  

  

Therefore,

  

  

Therefore,

​b)Find the quartiles Q1 & Q2 using the Tukey method.

Answer: The data in ascending order is:

To calculate the Q1 using the Tukey method, we need to consider the lower half of the given data i.e., first 13 observation's of the data:

Now the lower quartile Q1 is the middle number (the median) of the lower half.

The middle number of the lower half of the given data is 27.

Therefore,

is the middle quartile and it divides the data into two equal halves.

Since we have 25 observation's in the data, therefore the 13th item divides the data in two equal halves.

Therefore

c)Find the IQR using the quartiles from part b.

Answer: To find the IQR, we need to calculate the upper quartile

To calculate the Q3 using the Tukey method, we need to consider the upper half of the given data i.e., last 13 observation's of the data:

Now the upper quartile Q3 is the middle number (the median) of the upper half.

The middle number of the upper half of the given data is 39.

Therefore,

d)Find the standard deviation.

Answer: The standard deviation is given below:

Therefore, the standard deviation is

orchestra answered 1 year ago
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