Question

8. You and several friends visit the Old Faithful geyser in Yellowstone National Park. You record the interval times between eruptions in minutes. You get the following data. 81 81 86 87 89 92 93 94 95 96 97 98 98 10 10 106 a. How many interval times were recorded? b. What is the mean interval time? Round your answer to two decimal places. c. What is the median interval time? d. Identify the 5-number summary for this data. e. Construct a boxplot.

Answer 1

Given recorded interval times are (in minutes)

81,81,86,87,89,92,93,94,95,96,97,98,98,101,101,106

1) There is a total of 16 data points. So, total no. of interval times recorded were 16.

2) Mean interval time = (sum of all data points)/16= (81+81+86+........+ 106)/16= 1495/16 = 93.4375 ~ 93.44

3) For calculating median interval time,

first, we will arrange all the data points are in ascending order. Since given data points are already in sorted form. The number of data points is 16 which is even. So, take the mean of two middle terms (8th term & 9th term) as (94+95)/2 = 94.5

Median interval time = 94.5

4) Five number summary gives Minimum value, 1st quartile, Median, 3rd quartile, Maximum value.

Here, the Minimum & Maximum value of given data points is 81 & 106 respectively.

the 1st quartile is 1/4*16= 4th observation of given data points. i.e. 1st quartile = 87

Median is 94.5

the 3rd quartile is 3/4*16= 12th observation of given data points. i.e. 3rd quartile = 98

Hence, five number summary of data is (81, 87, 94.5, 98, 106).

5) Boxplot of given data points is

105 100 95 90 85 80