A survey of 44 JSE-listed companies recorded their dividend yields (as a percentage) for last year as shown in the following table:
|
5.3
|
4.8
|
3.1
|
4.1
|
6.1
|
4.1
|
3.2
|
4.6
|
7.6
|
1.6
|
|
4.6
|
1.9
|
4.8
|
2.9
|
1.5
|
5.1
|
2.8
|
3.6
|
3.3
|
5.5
|
|
2.8
|
4.2
|
3.6
|
3.1
|
5.9
|
2.9
|
3.6
|
4.1
|
4.9
|
2.7
|
|
3.7
|
7.1
|
6.2
|
2.8
|
5.1
|
3.8
|
3.4
|
3.9
|
5.8
|
6.3
|
|
6.8
|
4.3
|
5.1
|
5.4
|
|
|
|
|
|
|
(a) Define the random variable and its data type.
(b) Use Excel's Data > Data Analysis > Descriptive Statistics option to find the mean, median, mode, standard deviation and skewness measure of the dividend yields of the JSE-listed companies.
(c) Interpret the meaning of each descriptive statistical measure in (b).
(d) Which central location measure would you use to report on the dividend yields of companies? Why?
(e) Use Excel's Data > Data Analysis > Histogram option to compute a numeric frequency distribution and a histogram of the dividend yields of the sampled JSE companies. (Hint: Use the bin range given in the database.)
(f) Use Excel's function key operations (MIN, MAX, MEDIAN and QUARTILE) to compute the five-number summary table.
(g) Construct a box plot of the dividend yields of the JSE-listed companies and interpret the profile of the dividend yields declared by JSE companies last year.
(h) What was the minimum dividend yield declared by the top 10% of JSE companies? (Hint: Use thePERCENTILE function key.)
(i) What percentage of JSE companies did not declare more than a 3.5% dividend yield last year? (Hint: Compute the ogive to find the cumulative percentages.)