The geyser Old Faithful in Yellowstone National Park alternates period

Fenian41

Fenian41

Answered question

2021-11-27

In Yellowstone National Park, the geyser Old Faithful alternates between bursts of eruption, which typically last 1.5 to 4 minutes, and periods of dormancy, which last much longer. The table below represents the durations, in minutes, of 60 dormancy periods that occurred during a recennt year. 
919999839985909688938888921165910190711039782918989949461966610590938892869395839099899490959310596921019194929486889990998492 
1. Create a frequency distribution for the data that is grouped into 6 classes. There should be a column for relative frequency. 
2. Calculate the mean of the grouped data.

Answer & Explanation

Ceitheart

Ceitheart

Beginner2021-11-28Added 14 answers

Step 1 
The given data is 
59, 61, 66, 71, 82, 83, 83, 84, 85, 86, 86, 88, 88, 88, 88, 88, 89, 89, 89, 90, 90, 90, 90, 90, 90, 91, 91, 91, 92, 92, 92, 92, 92, 93, 93, 93, 93, 94, 94, 94, 94, 94, 95, 95, 96, 96, 96, 97, 99, 99, 99, 99, 99, 99, 101, 101, 103, 105, 105, 116 
Step 2 
Solution : 
A) Arrange the given data in ascending order : 
59, 61, 66, 71, 82, 83, 83, 84, 85, 86, 86, 88, 88, 88, 88, 88, 89, 89, 89, 90, 90, 90, 90, 90, 90, 91, 91, 91, 92, 92, 92, 92, 92, 93, 93, 93, 93, 94, 94, 94, 94, 94, 95, 95, 96, 96, 96, 97, 99, 99, 99, 99, 99, 99, 101, 101, 103, 105, 105, 116 
Class width=Maximum value-minimum valuenumber of classes 
=116596 
=9.5 
=10 
Relative frequency=Number of frequencyTotal number of frequency 
Frequency distribution table: 
ClassFrequencyRelative frequency596833/60=5%697811.67%79881220%89983253.3%991081118.3%10911811.67%Total60 
Step 3 
B) Mean: 
Midpoint: upper boundary+lower boundary2 
ClassFrequency(f)midpoint(x)5968363.56978173.579881283.589983293.59910811103.51091181113.5Totaln=60  
Mean =fxn 
=63.53+73.51+83.512+93.532+103.511+113.516 
=551060 
=91.833 
Mean =91.833

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