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

Question

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 right. Complete parts a) through d). Find the quartiles using technology. Q1 = 25 and Q3 = 37 Find the quartiles using the Tukey method. Q1 = 25 and Q3 = 37 Find the IQR using the quartiles from part b. IQR = 12 Find the standard deviation. The standard deviation is (Round to three decimal places as needed.)

Explanation / Answer

Sol:

The first quartile of the data set is 25.

Explanation

The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

11   14   21   22   23   25   25   28   29   31   31   31   31   32   32   34   35   36   37   43   43   43   44   48   48   

So, the bottom half is

11   14   21   22   23   25   25   28   29   31   31   31   

The median of these numbers is 25.

Solutionb:

The third quartile of the data set is 40.

Explanation

The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

11   14   21   22   23   25   25   28   29   31   31   31   31   32   32   34   35   36   37   43   43   43   44   48   48   

So, the upper half is

32   32   34   35   36   37   43   43   43   44   48   48   

The median of these numbers is 40.

Solutionc:

The interquartile range of the data set is 15.

Explanation

The interquartile range is the difference between the third and first quartiles.

The third quartile is 40.

The first quartile is 25.

The interquartile range = 40 - 25 = 15.

Solutiond:

The standard deviation of the data set is:

=9.7182

Explanation

To find standard deviation we use the following formula

=sqrt[(xiX¯¯)2/n1]

We will compute this formula in 4 steps.

Step 1: Find the mean. (X¯¯¯)

Here: X¯¯¯=31.88.

Step 2: Create the following table.

Step 3: Find the sum of numbers in the last column to get.

(xiX¯¯¯)2=2266.64

Step 4: Calculate using the above formula.

=sqrt[(xiX¯¯¯)2/n1]

=2266.64/251

9.7182

std dev=9.718

data data-mean (data - mean)2 21 -10.88 118.3744 32 0.12 0.0144 34 2.12 4.4944 29 -2.88 8.2944 31 -0.88 0.7744 31 -0.88 0.7744 31 -0.88 0.7744 14 -17.88 319.6944 28 -3.88 15.0544 11 -20.88 435.9744 37 5.12 26.2144 22 -9.88 97.6144 44 12.12 146.8944 48 16.12 259.8544 25 -6.88 47.3344 25 -6.88 47.3344 23 -8.88 78.8544 31 -0.88 0.7744 35 3.12 9.7344 32 0.12 0.0144 36 4.12 16.9744 43 11.12 123.6544 43 11.12 123.6544 43 11.12 123.6544 48 16.12 259.8544

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