Question

The following experimental data represent a distribution of driving speeds (in miles per hour) at which individuals were travelling on a highway: 64 68 79 80 64 70 76 67 72 65 73 65 67 65 70 62 67 68 65 64 7) Calculate the 25th, 50th, and 75th percentiles for the data. Based on this, calculate the "interquartile range" (i.e., IQR) for these results 8) Construct a boxplot (box-and-whisker plot) for the data using the technique I described in the video lectures (as I noted in the lecture, you should ignore the technique they present in your textbook). Are there any outliers in the data? Explain what the graph depicts 9) Assuming that the data are calculate the z-score for a value of 70 in the dataset. Interpret the z-score (i.e., what does it indicate?). Based on the standard normal (z) distribution, what percentage of the drivers drove as fast or faster than that value in the experiment? relatively close to being normally distributed, 10) Looking back at all of the descriptive statistics that you've calculated, how would you describe the results of this experiment? Were the subjects fairly similar in terms of their driving speeds? Fairly different? Explain and be specific!

Answer 1

First we have to arrange the given data in ascending order.

Data
62
64
64
64
65
65
65
65
67
67
67
68
68
70
70
72
73
76
79
80

7) Total number of observations n = 20

25^th percentile = 5^th observation in the data as n = 20, 25^th percentile = 20*0.25 = 5

25th percentile = 65

50^th percentile = 20*0.5 = 10th observation

50^th percentile = 67

75^th percentile = 71.5

Inter quartile range IQR = 75^th percentile - 25^th percentile = 70 - 65 = 5.

IQR = 6.50

8) Box and whisker plot

Boxplot of Given Data 80 75 70 65 60 Data

There are no outliers in the data. Range is very much higher than IQR.

9) Mean $\mu$ = = 68.55

=1 η.

Standard deviation $\sigma$ = = 5.10

(aiT) 2 n 1

Z score

Z =
LL
=
70 68.55 5.1
= 0.284

z-score of 0.284 represents that there is a 61.18 % of the observations are lesser than X = 70.

10) Descriptive statistics are

Descriptive Statistics: Driving speed

Variable	Mean	SE Mean	StDev	Minimum	Q1	Median	Q3	Maximum	Range	IQR
Data	68.55	1.14	5.10	62.00	65.00	67.00	71.50	80.00	18.00	6.50

Histogram of Driving Speeds 7 6 5 4 2 1 0 62.5 65.0 67.5 70.0 72,5 75.0 77.5 80.0 Data Frequency LC

The driving speeds are fairly different.