) = 0, relevant to this concept?(b) Show that Σ(X–
) = 0 for the following sample of scores: 2,5,7,8,13. KNR 445
Statistical Applications in Science & Technology
Assignment
Measures of Central Tendency
The purpose of this lab is to introduce the procedures for calculating measures of central tendency, and for selecting the most appropriate measure. You will use your CDC data file that includes the variable "Region" .
Measures of Central Tendency
Identifying the "typical" score of a distribution (sample or population) has
lead to the identification of three measures of central tendency: the mode, the median and
the mean. Each measure has a useful application, typically specific to one kind of data.
Misuse of the measures is often a point of heated discussion among statisticians and users
of data.
Homework
1. For
each of the following sets of scores, find the mode, the median, and the mean:
(a)
12, 10, 8, 22, 8
(b)
14, 12, 25, 17
(c)
10, 6, 11, 15, 11, 13
2. In
the following quotation, taken verbatim from a company newsletter, the author
was attempting to provide statistical enlightenment:
One of the most misused words is the word "average."
It is often confused with "mean."
The difference is this: If five products sell for $2, $3, $5, $8, and
$67, the average price is $17. The
median, or mean, price is $5, the $5 price being the middle price―two
prices are higher and two are lower: The
average of a series may or may not be the middle.
Your task: Comment on the accuracy of the author's remarks, sentence by
sentence.
3.
(a) What is meant by the
"balance point: of a distribution of scores?
How is the expression,
∑(X–
) = 0, relevant to this concept?
(b) Show
that Σ(X–
) = 0 for the following sample of scores: 2,5,7,8,13.
*4. Comment on the probable shape for each of the
following distributions:
(a)
= 52, Mdn = 55, Mo = 60
(b)
= 78, Mdn = 78, Mo = 78
(c)
= 50, Mdn = 50, Mo = 60, 40
(d)
= 28, Mdn = 26, Mo = 20
5.
State the likely relative positions of the mean, median, and mode for the
following distributions.
(a.) family income in a
large city.
(b)
scores on a very easy exam
(c)
heights of a large group of 25-year-old males
(d)
the number of classes skipped during the year for a large group of
undergraduate students
6. A newspaper editor once claimed that more than half of American families earned a below-average income. Could this claim possibly be correct? (Explain.)
7. At a local K-6 school, the four K-2 teachers have a mean of 15 students per class, while the five teachers for grades 3-6 have a mean of 18 students per class. What is the mean number of students across the nine teachers in this school?
8.
X = 23, Mdn = 23, Mo = 31 for a particular distribution of 25 scores. It was subsequently found that a scoring mistake had been
made: one score of 43 should have been a 34.
(a)
What is the correct value for
?
(b)
How would the Mdn and Mo be affected by this error?
SPSS Questions:
1. Find and list the procedures in SPSS which allow you to calculate the mean and other measures of central tendency.
2. Calculate the mean, median and mode for the variable Region.
a. What type of data is the variable "Region"?
b. Interpret the mean, median and mode values from the SPSS output.
c. Which, if any, of the measures of central tendency is most appropriate for this type of
data?
SPSS output
3. This question will use the data in the variable Smoker Deaths.
a. Calculate the population mean for the variable Smoker Deaths.
b. For each of your six regions, calculate the mean of the variable Smoker Deaths.
c. BY HAND, calculate the mean of the six region means. Compare it to the population mean.
d. Compare the population mean to the individual region means:
i. How many region means are equal to the population mean?
ii. How many region means are less than the population mean?
iii. How many region means are greater than the population mean?
SPSS Output
4. This question will use the data in the variable Tax per Pack:
a. Calculate the population mean for the variable Tax per Pack.
b. Create a new variable, TaxUp, by multiplying each state tax by 10, and calculate the
population mean for this new variable.
c. Create a new variable, TaxDown, by dividing each state tax by 10, and calculate the
population mean for this new variable.
d. Using the Custom Tables procedure found under Analyze, create
a table of the mean values of Tax per pack, TaxUp and TaxDown (optional).
e. Compare the mean values calculated in a, b and c and presented in d.
SPSS Output