Question

The management requested that a rollercoaster ride time shouldn’t take longer than 5 minutes on average; 10 volunteers recorded their rollercoaster ride time (in seconds). They reported the following set of data:

Name	Time	Z-Score
Simpson	300
Scott	290
Maurice	320
Dario	310
Vincent	390
Daniel	380
Alexander	375
Toni	290
Ivan	260
Johan	300

a. Calculate the following descriptive statistics (Briefly explain). NOTE: you can use Excel in your computation.

Mean
Median
Mode
Who’s time is in the lowest quartile?
Who’s time is in the uppermost quartile?
Interquartile Range
Range
Standard Deviation
Variance

b.   Compute the z-scores and enter them in the first given table. Give the formula you used.

Answer 1

Solution:-

Given data:-

260

290

290

300

300

310

320

375

380

390

a.) Mean=(260+290+290+300+310+320+375+380+390)/10

=321.5

Median=(300+310)/2

=305

Mode=This is bimodal data

Mode1=290

Mode2=300

Lower half of the data:

260

290

290

300

300

Lower Quartile=median of first half of data

=290

Who’s time is in the lowest quartile=Toni

upper half of the data:

310

320

375

380

390

Upper Quartile=Median of the Upper half of the data

=375

Who’s time is in the uppermost quartile= Alexander

Interquartile Range=Upper Quartile-Lower Quartile

=375-290

=85

Range=390-260=130

Standard Deviation=44.475

Variance =(Standard Deviation)²

=44.475*44.475

=1978.056

Mean	321.5
Median	305
Mode	290,300
Who’s time is in the lowest quartile?	290
Who’s time is in the uppermost quartile?	375
Interquartile Range	85
Range	130
Standard Deviation	44.475
Variance	1978.056

b.)

Z Score=(X-Mean)/Std.Deviation

Z score (for Simpson)=(300-321.5)/44.475

=-0.48

similarly

Name	Time	Z-Score
Simpson	300	-0.48
Scott	290	-0.71
Maurice	320	-0.03
Dario	310	-0.26
Vincent	390	1.54
Daniel	380	1.32
Alexander	375	1.20
Toni	290	-0.71
Ivan	260	-1.38
Johan	300	-0.48