1 answer

A cellular phone company monitors monthly phone usage. The following data represent the monthly phone use...

Question:

A cellular phone company monitors monthly phone usage. The following data represent the monthly phone use in minutes of one p

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). 339 456 425 478 549 556 505 544 446 472 449 521 545 445 468 367 431 394 408 496 (a) Determine the standard deviation and interquartile range of the data Sul (Round to two decimal places as needed.)

Answers

Answer :

Given data is :

Sample size n = 20

339 456 446 472 449
425 478 521 545 445
549 556 468 367 431
505 544 394 408 496

From the data we need to find the standard deviation S :

First find mean = \bar{X}  - X/n

= [339 + 456 + 446 + 472 + 449 + ............ + 408 + 496] / 20

= 9294 / 20

= 464.7

\bar{X} = 464.7

Standard deviation= S = (1 – 4)/(X-X)

= (339 - 464.7)2 + (456 - 464.7)2 + (446 – 464.7)2 + (472 - 464.7)2.............. + (408 - 464.7)2 + (496 - 464.7)2/20 - 1)= (-125.7)2 + (-8.7)2 + (-18.7)2 + (7.3)2.............. + (-56.7)2 + (31.3)2/19== 15800.494 75.69 +349.69 + 53.29+..... + 3214.894979.69/19= 71524.2/19

= V3764.432

=61.355

S = 61.355

Next we need to find interquartile range of data :

Take first 10 numbers :

339 456 446 472 449 425 478 521 545 445

Sort this data into ascending order to find median :

339 425 445 446 449 456 472 478 521 545

Median of first 10 data numbers= Q_{1} = (449 + 456) / 2 = 905 / 2 = 452.5

Q_{1} = 437

Now take remaining 10 numbers :

549 556 468 367 431 505 544 394 408 496

We need to sort the above data to find the median :

367 394 408 431 468 496 505 544 544 549

Median of above 10 numbers = ( 468 + 496) / 2 = 964 / 2 = 482

Q3 = 482

Q_{2} is nothing but the median of all complete data.

Formula to calculate interquartile range of data is :

IQR = Q3 - Q1 = 482 - 437 = 45

IQR = 45

.

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