Question

Assume you work for OSHA (Occupational Safety and Health Administration) and have complaints about noise levels from some of the workers at a state power plant. You charge the power plant with taking decibel readings at 2 different areas of the plant at different times of the day and week. The results of the data collection are listed. The safe hearing level is approximately 120 decibels

Area1	Area 2
30	59

12	63
35	81
65	110
24	65
59	112
68	132
57	145
100	163
61	120
32	84
45	99
92	105
56	68
44	75

Question 1. Calculate mean, median, mode, and standard deviation to describe the data of collected data for Area 1 using Data>Data Analysis>Descriptive Statistics. Make precise interpretations of each statistical measure in Text Box (Insert>Text Box). (2 points)

Question 2. Calculate first, second and third quartiles for Area 2 (Q1, Q2, Q3, Excel: =QUARTILE()) and interquartile range (IQR=Q3-Q1). Make precise interpretations of each statistical measure. (2.0 points)

Question 3. Determine class width and create a frequency table with 4 classes for Area 1. The table should have the following headings (2.0 points): Class limits Frequency Relative frequency Cumulative frequency

Question 4. Draw bar chart (based on the data from question 3) describing the obtained relative frequency. Provide description. (0.5 point)

Question 5. Make recommendations about which plant area workers must be provided with protective ear wear. (1.0 point)

Answer 1

Q1:

Area 1
Mean	52
Standard Error	6.237368
Median	56
Mode	#N/A
Standard Deviation	24.15722
Sample Variance	583.5714
Kurtosis	-0.01606
Skewness	0.419634
Range	88
Minimum	12
Maximum	100
Sum	780
Count	15

Mean=52 i.e. average reading of Area 1 is 52.

Median=56 i.e. 50% of readings of Area 1 have noise level more than 56 or 50% reading of Area 2 have noise level less than 56.

Since each observation appears exactly one so mode does not exist,

Standard deviation=24.15722 and it measures the deviation of the readings of Area 1 from average reading of Area 1.

Q2:

Q1=	71.5
Q2=	99
Q3=	116
IQR=Q3-Q1=	44.5

25% of readings of Area 2 below 71.5, 50% of readings of Area 2 below 99, 75% of readings of Area 2 below 116 and middle 50% readings of Area 2 lies between 71.5 and 116. IQR measures the variation of readings of Area 2.

Q3:

Class boundary	Frequency	Relative frequency	Cumulative frequency
12--34	4	0.2667	4
34-56	4	0.2667	8
56-78	5	0.3333	13
78-100	2	0.1333	15
Total	15	1

Q4:

Q5: From above we see that median of Area 1 <median of Area 2, hence Area 1 provides with protective ear wear.