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)

321 423 417 416 508

378 390 491 552 387

325 430 329 454 547

337 345 490 340 356

(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)

Answer 1

(A) For standard deviation, we will first calculate the mean value of the data set

Mean = (sum of all values)/(total number of values)= (321+423+...+340+356)/20 = 8236/20 = 411.80

Formula for standard deviation is given as

where xi are given data values and x(bar) = sample mean = 411.80 and n is sample size = 20

setting the values, we get

this gives us

Therefore, standard deviation = 74.36 (rounded to 2 decimals)

we know that relationship between IQR and standard deviation is given as

IQR = 1.34*(standard deviation)

we have standard deviation = 74.36

so, IQR = 1.34*74.36 = 99.6424 or 99.64 (rounded to 2 decimals)