Question

Braking Reaction Times: Histogram Listed below are sorted braking reaction times (in 1>10,000 sec) for male and female subjects (based on data from the RT-2S Brake Reaction Time Tester). Construct a histogram for the reaction times of males. Use a class width of 8 and use 28 as the lower limit of the first class. For the horizontal axis, use class midpoint values. Does it appear that the data are from a population with a normal distribution?

Males	28	30	31	34	34	36	36	36	36	38	39	40	40	40	40	41	41	41
	42	42	44	46	47	48	48	49	51	53	54	54	56	57	60	61	61	63
Females	22	24	34	36	36	37	39	41	41	43	43	45	45	47	53	54	54	55
	56	57	57	57	58	61	62	63	66	67	68	71	72	76	77	78	79	80

Short answer

The histogram for the male braking reaction times is shown below:

The graph shows that the male braking reaction times follows a normal distribution.

Step-by-step solution

Given information

Data for brake reaction times for males and females are given.

Identify the frequency distribution for the reaction time of males

The class width is 8.

The lower limit of the first class is 28.

The lower limit of the first interval is 28, and hence, the upper limit of the first interval is $28+8=36$. Consecutively, the lower limit (L.L)of the second interval will be 36, and the upper limit (U.L) will be44, and so on.

Count the observations that lie between the intervals from the dataset and mark them under the frequency column.

The midpoint for each interval is computed as shown:

$m=\frac{L.L+U.L}{2}$

The obtained frequency distribution is shown below:

Lower limit (L.L)	Upper limit (U.L)	Frequency (f)	Midpoint (m)
28	36	5	32
36	44	15	40
44	52	7	48
52	60	5	56
60	68	4	64

Sketch the histogram

Steps to sketch the histogram:

1. Draw the horizontal axis for the midpoints and the vertical axis for the frequency of male braking reaction time.
2. For each midpoint and frequency, mark a column such that the extent for each column is defined by the lower and upper limits on the horizontal axis, while the height is defined by the frequencies.
3. The resultant histogram is shown below.