Review of measures of central tendency and dispersion.

1. Happy π Day!
Pi Pie by sarako

2. Let's apply what we've learned ... HOMEWORK
The mean math marks and standard deviation for two classes are shown
below. Assume that 68 percent of the marks in each class are within one
standard deviation of the mean mark.
mean mark (μ) standard deviation (σ)
Class A 74 4
Class B 72 8
(a) In which class is the set of marks more dispersed?
(b) Bert in Class A and Beth in Class B each have a mark of 82%. How many
standard deviations are they from their class means? Who appears to have the
better mark?

3. 9
HOMEWORK
The following numbers represent the number of cars sold by Metro Motors in one
week:
Monday Tuesday Wednesday Thursday Friday Saturday
4 5 8 9 7 9
1. Determine the following statistics:
(a) mean (b) mode (c) median (d) range
2. Which measure of central tendency may be the least significant? Explain.

4. HOMEWORK
The two sets of data show the weights of potatoes in bags. There are six bags in
each set.
Set #1 49 51 48 52 47 53
Set #2 40 60 45 55 35 65
The mean weight of each set of bags is 50 pounds. Which set has the greater
standard deviation? How do you know? (Do not do any calculations.)

5. HOMEWORK 78 92 62 52 65 59
A class of 30 students received the following
marks in a mathematics examination. Calculate 53 63 68 73 71 63
the mean, median, range, and standard deviation. 69 74 73 81 55 71
75 81 84 77 80 75
41 57 91 62 65 49

6. Measures of Dispersion (Variability)
determine how quot;spread outquot; or variedquot; a set of data is.
Standard Deviation (σ): What's the difference between quot;σquot; and quot;squot;?
The symbol for standard deviation of a population or large sample is
quot;σquot; (sometimes written as quot;σx quot;), and the symbol for standard deviation
of a sample is 's'. A large sample is defined as a sample with 30 or
more data items. In this course, we will use only quot;σquot; (sigma), which
represents the standard deviation of the population.
Let's take a look at a visual explanation of why we calculate
the standard deviation this way ...

7. Peter's goal is to maintain his marks at least 2.5 standard deviations above the
mean in all of his subjects. Determine the minimum marks he must obtain in each
subject.
Subject Mean Standard Deviation Minimum Mark
Chemistry 66 7
English 62 12
Math 68 8
Physics 73 4

8. Teacher Adams has a large math class with 38 students. The mean class mark
is 65 percent, and the standard deviation is 18 percent. Do you think this is
an easy class for Teacher Adams to teach? Explain.