Question 3 a) The following stem-and leaf display of the dividend yields ($) for common stocks Stem-and-Leaf Display N = x Leaf Unit = 1.0 5 2 33444 11 2 668899 (14) 3 00112223344444 y 3 56778899 12 4 0002344 5 4 66789 i. Determine the value of x and y. ii. What is the value of the median? iii. Find the modal yield of this data set. b) The table below is based on the Stem and leaf diagrams showing dividend yields ($) for common stocks Dividend Yielded ($) Frequency 20-24 5 25-29 6 30-34 14 35-39 x 40-44 7 45-49 5 i. Use the stem and leaf diagram in 3a) to determine the value of x. ii. Using the table above to calculate a) the sample mean of the dataset. b) the mode of the dataset. c) the sample variance of the dataset.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Question 3
a) The following stem-and leaf display of the dividend yields ($) for common stocks
Stem-and-Leaf Display
N = x Leaf Unit = 1.0
5 2 33444
11 2 668899
(14) 3 00112223344444
y 3 56778899
12 4 0002344
5 4 66789
i. Determine the value of x and y.
ii. What is the value of the median?
iii. Find the modal yield of this data set.
b) The table below is based on the Stem and leaf diagrams showing dividend yields ($) for
common stocks
Dividend Yielded ($) Frequency
20-24 5
25-29 6
30-34 14
35-39 x
40-44 7
45-49 5
i. Use the stem and leaf diagram in 3a) to determine the value of x.
ii. Using the table above to calculate
a) the sample mean of the dataset.
b) the
c) the sample variance of the dataset.
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