Question

5. The driver's reaction time in response to a particular potential traffic hazard is the time required from the point of initial detection of the hazard in one’s field of view to the time that vehicle control components are actuated (such as the movement of one’s foot to the brake pedal). The following data represent the measurements of the driver’s reaction time in seconds for the male and female participants of the experiment:

0.50	0.49	0.45	0.54	0.44	0.49	0.51	0.48
0.51	0.53	0.51	0.63	0.69	0.76	0.76	0.85

(a) Calculate the sample mean of the data. Calculate the sample variance of the data. Calculate the corresponding standard deviation.

(b) Find the median and quartiles for the data.

(c) Construct a box plot of the data (use any software of your choice e.g. excel, Matlab, statistical etc.. Find the interquartile range and determine the number of outliers.

Answer 1

a. Sample mean is

Create the following table.

data	data-mean	(data - mean)2
0.50	-0.0713	0.00508369
0.49	-0.0813	0.00660969
0.45	-0.1213	0.01471369
0.54	-0.0313	0.00097969
0.44	-0.1313	0.01723969
0.49	-0.0813	0.00660969
0.51	-0.0613	0.00375769
0.48	-0.0913	0.00833569
0.51	-0.0613	0.00375769
0.53	-0.0413	0.00170569
0.51	-0.0613	0.00375769
0.63	0.0587	0.00344569
0.69	0.1187	0.01408969
0.76	0.1887	0.03560769
0.76	0.1887	0.03560769
0.85	0.2787	0.07767369

Hence

b. The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

0.44   0.45   0.48   0.49   0.49   0.50   0.51   0.51   0.51   0.53   0.54   0.63   0.69   0.76   0.76   0.85   

As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:

Median=

The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

0.44   0.45   0.48   0.49   0.49   0.50   0.51   0.51   0.51   0.53   0.54   0.63   0.69   0.76   0.76   0.85   

So, the bottom half is

0.44   0.45   0.48   0.49   0.49   0.50   0.51   0.51   

The median of these numbers is 0.49.

The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

0.44   0.45   0.48   0.49   0.49   0.50   0.51   0.51   0.51   0.53   0.54   0.63   0.69   0.76   0.76   0.85   

So, the upper half is

0.51   0.53   0.54   0.63   0.69   0.76   0.76   0.85   

The median of these numbers is 0.66.

c.

The interquartile range is the difference between the third and first quartiles.

The third quartile is 0.66.

The first quartile is 0.49.

The interquartile range = 0.66 - 0.49 = 0.17.

From box plot we see that there is no outliers