Question

A study of smartphone users shows that 68% of smartphone use occurs at home and a user spends an average of 410 minutes per month using a smartphone to interact with other people. Consider the following data indicating the number of minutes in a month spent interacting with others via a smartphone for a sample of 50 smartphone users. 351 352 353 354 357 360 367 367 368 369 372 374 384 387 387 388 390 394 401 402 404 405 407 413 416 417 422 424 430 430 430 431 435 436 437 441 444 445 445 446 448 458 460 461 464 464 468 468 469 470 i. What is the sample range? ii. If you are going to construct a frequency histogram and a relative frequency histogram with 6 classes, what is the appropriate class width in each class’s interval? Give an example of the first interval and the second interval for these intervals. Assume the first interval starts from 351. iii. Find the frequency and the relative frequency in the interval (391, 410).

What are the median, the 35th percentile, and the 92th percentile?

Write your answer with the format of ###.#, ###.#, ###.#, the first number is the median, the second number is the 35th percentile, and the third number is the 92th percentile.

Answer 1

(i)

Minimum value: 351

Maximum value: 470

Range = 470 - 351 = 119

(ii)

Since we need 6 classes so class width will be

Class width = 119 / 6 = 19.83

That is class width is 20.

Following table shows the frequency and relative frequencies:

Classes	Frequency, f	Relative Frequency, f/50
351-370	10	0.2
371-390	7	0.14
391-410	6	0.12
411-430	8	0.16
431-450	10	0.2
451-470	9	0.18
Total	50	1

(iii)

The frequency in interval (391, 410) is 6 and relative frequency is 0.12.

The median is middle value of ordered data set so median is average of 25th and 26th data values. That is median is

-----------

The 35th percentile is

Total number of data values: n = 50

So 35th percentile will be

Since 17th data value is 390 and 18th data value is 394 so requried percentile is

-----------------------

The 92th percentile is

Total number of data values: n = 50

So 92th percentile will be

Since 46th data value is 464 and 47th data value is 468 so requried percentile is

Answer: 416.5, 393.4, 467.7