A cellular phone company monitors monthly phone usage. The following data repres

Question

A cellular phone company monitors monthly phone usage. The following data represent the monthly phone use in minutes of one particular customer for the past 20 months. Use the given data to answer parts (a) and (b). (a) Determine the standard deviation and interquartile range of the data. s = (Round to two decimal places as needed) IQR = (Type an integer or a decimal) (b) Suppose the month in which the customer used 336 minutes was not actually that customer's phone. That particular months the customer did not use their phone at all, so 0 minutes were used. How does changing the observation 336 to 0 affect the standard deviation and interquartile range? What property does this illustrate? The standard deviation increases and the interquartile What property does this illustrate? Choose the correct answer below. Resistance Dispersion Empirical Rule Weighted Mean

Explanation / Answer

Enter the given data set in the Excel sheet.

The standard deviation of the data can be obtained using the Excel function STDEV () as below:

standard deviation = STDEV (336, 400, 559, 472, ... , 464, 396) = 75.27

The interquartile range is given by ( Q3 - Q1).

Thus, first we find the first and third quartile using Excel function Quartile (array, quart) as below:

Q3 = Quartile (336, 400, 559, 472, ... , 464, 396, 3) = 445.5

Q1 = Quartile (336, 400, 559, 472, ... , 464, 396, 1) = 369.25

Therefore,

interquartile = (Q3 - Q1) = ( 445.5 - 369.25) = 76.25

if we change 336 with 0, then there will be no change in inquartile range, however, the standard deviation will change.

The standard deviation increases and the inter quartile range is not affected.

This property is called dispersion as it measures the spread of data, that is, how the data is dispersed.

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