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 327 minutes was not actually that customers phone That particular month the customer did not use their phone at all so 0 minutes were used. How does changing the observation from 327 to 0 affect the standard deviation and interquartile range? What property does this illustrate? The standard deviation and the interquartile range What property does this illustrate? Choose the correct answer below. Empirical Rule Resistance Weighted Mean Dispersion

Explanation / Answer

a)

Since we have to find IQR arrange the numbers in ascending order i.e. from the lowest to the highest otherwise it's not required.

The formula for sd^2= [ summation X^2 - n( mean of X)^2]/ (n-1). Some text books use only "n" and not "n-1." but the latter is more accurate. So use n-1.

Mean of X = Summation X/ n = 8513/20 = 425.65
Summation X^2= 3742319

SD^2= [ 3742319 - 20(425.65^2)]/(20-1)
= [ 118760.6]/19
= 6250.555
SD = sqrt(6250.555)
SD = 79.06

Therefore, the standard deviation is 79.06.

Q1 = (n+1)4 th value
Q1 = 21/4 th value
Q1 = 5.25 th value
Q1 = 5 th value +0.25[6th val - 5th val]
Q1 = 347 + 0.25[348 - 347]
Q1 = 347.25

Q3 = 3(Q1 th value)
Q3 = 3(5.25 th value)
Q3 = 15.75 th value
Q3 = 15 th value +0.75[ 16th - 15th values]
Q3 = 477 + 0.75[ 513 - 477] { See the order of the no’s for values}
Q3 = 504

IQR = Q3 - Q1        

= 504 – 347.25

IQR = 156.75

b)

The standard deviation increases (Sx without 327) and the interquartile range is not affected.

What property does this illustrate?

Resistance.

322 323 327 342 347 348 368 383 414 418 430 445 448 456 477 513 521 533 543 555

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