stastitics question

Question

The local amusement park was interested in the average wait time at their most popular roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line between 2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times recorded were as follows (in minutes). Interpret the box plot and its numerical statistics. Also, determine how the skewness of this data set explains the distribution curve.

118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118 

 

Answer 1

The 5-statistics of the box plot are: minimum, maximum, median, 1st and 3rd quartiles.

First put the data in ascending order

45, 99, 108, 116, 118, 118, 118, 119, 120, 121, 124, 130, 148

The minimum value is 45

The maximum value is 148

To find the location of the value corresponding to a percentile use the formula:

x (n+1), where x is the percentile and n is the number of data points.

---

100

The median is the 50th percentile, so for 13 values, the median location is 50 (13 + 1) = 7

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

100

The 7th value is 118, so the median is 118.

The 1st quartile is the 25th percentile, so the 1st quartile location is 25 (14)

--------- = 3.5

100

In this case the 1st quartile is the average of the 3rd and 4th data values = 108 + 116/ 2 = 112.

The 3rd quartile is the 75th percentile, so the 1st quartile location is 75 (14)

--------- = 10.5

100

In this case the 3rd quartile is the average of the 11th and 12th data values = 121 + 124/ 2 = 122.5

The median is closer to the 3rd quartile, which means the distribution is skewed left.

Answer 2

118, 124, 108, 116, 99, 120, 14

8, 118, 119, 121, 45, 130, 118 

n=14 observations

Median of the first 7 is 116; which is the

"first quartile".

Third quartile=121.

So: Q1=116

M=(108+116)/2=112

Q3=121