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                   Basic Statistics Mid Term Exam                                    

(1 Hour)

Question 1:

For each of the following statements, state whether it is True (T) or False (F) and if it is false, state the correct statement:

1 - There four levels of measurement: nominal, ordinal, interval and ratio. The lowest is the ratio level and the highest is the nominal level.

2 - If a set of data consists of 100 observations, then the number of classes suggested is 7 classes.

3 - The stem and leaf display can be used to display both quantitative and qualitative data.

4 - The basic charts that will help portray a frequency distribution graphically are the histogram, the line charts, the pie charts, the frequency polygon and the cumulative frequency polygon.

5 - A set of data ha only one mean, one median and one mode.

6 - Σ (x - median) = 0   and Σ |x - x bar| = 0.

7 - The mean can be computed for all levels of measurements.

8 - The mean, median and mode are not affected by extremely large or small values.

9 - Two events A1 and A2 are said to be independent if P (A1 ∩ A2) = 0.

10  - If P (A1 U A2) = 0.75, P (A1) = 0.30, then P(A2) = 0.40 if A1 and A2 are mutually exclusive.

11 - µ1 = x bar and µ2 = σ²

12 - In frequency distributions with unequal width, one has to modify the frequencies when calculating the mean, the median and the mode.

Question 2:

a) The following is the frequency distribution of the annual sales (in thousand pounds) of 50 stores:

   1 - Calculate X bar, median and the mode numerically and illustrate their relative positions graphically.

   2 - Calculate the coefficient of variation and the coefficient of skewness.

   3 - Portray a less than cumulative frequency polygon. Fifty percent of the stores had annual sales less than what amount?

b) Given that:

   X bar =12 ,   C.V. = 25 ,    Σ X³ = 59940 ,    Σ X = 360.

   Calculate the coefficient of skewness α1.