MAT 1272 Statistics, SP2014

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• PE1.12
• #13693

Ezra Halleck
Participant

The following data give the speeds (in miles per hour) of 12 cars traveling on a highway.
67 71 57 54 69 74 77 62 61 59 58 63
a. Order the data.
b. Calculate the values of the three quartiles.
c. Find the (approximate) value of the 40th percentile.
d. Find the percentile rank of 62.
e. Construct a box-and-whisker plot.
f. Is the data set symmetric, skewed to the right or skewed to the left?

#17644

Participant

A)Order the data: 54,57,58,59,61,62,63,67,69,71,74,77
B)values of the three quartiles=Q1=58.5 Q2=62.5 Q3=70
C)value of 40th percentile: x=4/100(12+1)=5.2
d)Percentile rank of 62: 5/12×100=42%
e)
f) This data set is skewed to the right because the mean is greater than the median.

#17698

vivian gomez
Participant

Can somebody tell me why the Q1= 58.5 I thought it will only be 58. What did you guys did sum 57+58 and divide by 2?

I will appreciate your help here. thanks

#17703

Ezra Halleck
Participant

As I indicated in class, there are many small variations on the procedure of how to get these items. To keep it simple, to find Q1, I am asking that you find the median of the first half of the data. The first half of the data consists of
54, 57, 58, 59, 61, 62
It’s median is (58+59)/2=58.5

For the percentile, the formula is often
n=P/100*N+.5 where P is the percentile and N is the number of data points.
Here we get n=40/100*12+.5=5.3, which rounded to the nearest integer is 5.
In other words the 40th percentile is the 5th element which is 61

Finally, to determine the skewing, you need the mean (not calculated here) together with the median or the box and whisker plot (not here).

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