Alan is a facility manager who carried out a study about the monthly electricity bill (in HK$100) of the shop. He then randomly selected previous 48 months' data for analysis and listed as follows

2.34 4.11 5.5 5.3 5.99 4.07 4.05 6.11 2.71 5.59 6.55 10.07 + 0.1 7

1.46 6.79 2.95 0.01 7.49 6.59 7.36 3.79 3.64 6.73 6.61 10.08 + 0.1 0

7.99 9.2 6.35 5.99 9.57 8.51 8.32 4.01 5.03 6.28 12.01 10.09 + 0.1 4

7.6 5.93 8.93 8.56 7.64 8.26 8.07 6.44 9.73 6.42 9.11 10.06 + 0.1 5

Suppose a frequency table is constructed using 6 classes. Use the smallest data value from the above sample as the lower class limit of the first class.

(a)Find the class width and Class Limits,Class Boundaries,Midpoint,Frequency,Cumulative Frequency

(b)Estimate the mean and the variance based on the frequency table constructed in part (a). Correct your final answers to 3 decimal places.

(c)Suppose at least 84% of the monthly electricity bills are within the interval (in HK$100) from X to Y. By using the Chebyshev'stheorem, find the interval (in HK$100) from X to Y of the monthly electricity bill around the mean. Correct your final answers to 3 decimal places.

A researcher wants to study whether drinking coffee can make students get a better grade in SEHH0108 Statistics in ABC Community College. He randomly selected four academic programmes of ABC Community College, and then included all students from these selected programmes in the sample. His survey included the following three questions:

A1. How many cups of coffee do you drink every week?

A2. Did you take/enroll in SEHH0108 Statistics last year? [Y = YES, N = NO]

A3. What grade did you get in SEHH0108 Statistics last year?

(a) Define the population in this study.

(b) Identify the sampling technique being used in this study.

(c) For each of the above questions (QA1 to QA3), determine whether the variable is qualitative or quantitative. In addition, indicate the level of measurement.