Question

Part 2 (Numerical Descriptive Techniques)

1. The following data represent the ages of a sample of 25 employees from a government department. Enter this data on a sheet called Employee Data.

      31        43        56        23        49        42        33        61        44        28

      48        38        44        35        40        64        52        42        47        39

      53        27        36        35        20

1. 1. Find the median age.
   2. Find the lower quartile of the ages.
   3. Find the upper quartile of the ages.
   4. Compute the range and interquartile range of the data.
   5. Compute the sample mean ag
   6. Construct a box plot for the ages and identify any outliers. Call the worksheet Question 12 Box Plot, and move it so it immediately follows the Employee Data sheet.
2. You are given the following sample data. Enter it on a sheet called Question 13.

x	420	610	625	500	400	450	550	650	480	565
y	2.80	3.60	3.75	3.00	2.50	2.70	3.50	3.90	2.95	3.30

1. Calculate the covariance and the correlation coefficient.
2. Comment on the relationship between x and y.
3. Draw the scatter diagram and plot the least squares line. Name this sheet Question 13 Scatter Diagram and make sure it follows the sheet called Question 13.

14. A sample of eight observations of variables x and y is shown below. Enter the data on a sheet called Question 14.

x	5	3	7	9	2	4	6	8
y	20	23	15	11	27	21	17	14

      a.   Calculate the covariance and the coefficient of correlation, and comment on the relationship between x and y.

      b.   Draw the scatter diagram and plot the least squares line. Name this sheet Question 14 Scatter Diagram and make sure it follows the sheet called Question 14.

c.   Estimate the value of y for x = 6.

Answer 1

Ordering the data from least to greatest, we get:

20   23   27   28   31   33   35   35   36   38   39   40   42   42   43   44   44   47   48   49   52   53   56   61   64   

a) Median = ( N+1)/2 th data i.e 13th data t.e, 42

So, the median is 42 .

b)  

So, the bottom half is

20   23   27   28   31   33   35   35   36   38   39   40   

The median of these numbers is 34.

Q₁= 34

c)

The upper half is

42   43   44   44   47   48   49   52   53   56   61   64   

The median of these numbers is 48.5.

Q₃= 48.5

d_)

Range = Maximum- Minimum = 64-20 = 44

Inter quartile range = Q₃- Q₁ = 48.5 - 34 = 14.5

e)  

The mean of a data set is the sum of the terms divided by the total number of terms. Using math notation we have:

Mean=Sum of terms/Number of terms

= 1030/ 25 = 41.2

f) Box plot

  There is no outlier.