In the year 2000, the average salaries of elementary school teachers in Oregon,
Washington and Alaska were (in thousands USD) 40.9, 41.1 and 47.3. Given that there
were 19.7, 28.1 and 5.3 thousand teachers in these states. Find the average salary of all
the elementary school teachers in the three states.
A wholesaler sold 575, 410 and 520 microwave ovens at prices (in USD) 75, 125 and 100
respectively. What is the mean price of the ovens sold?
If somebody invests TL 1,000 at 7%, TL 3,000 at 7.5% and TL 16,000 at 8%.
What is the overall percentage yield of these investments?
A researcher claims that each year, there is an average of 300
victims of identity theft in major cities. Twelve were randomly
selected, and the number of victims of identity theft in each city is
shown.
574
117
229
239
663
465
372
136
102
189
Can you conclude that the researcher was correct?
88
75
The number of employees of the municipalities in a certain area of a
country were given in the following table
#
202-204
205-207
208-210
211-213
214-216
217-219
Find the mean and modal class?
Frequency
2
7
16
26
18
4
THE MODE
- If a data set has only one value that occurs with greatest frequency
is said to be UNIMODAL
- If a data set has two values that occur with the same greatest
frequency is said to be BIMODAL
- If a data set has more than two values that occur with the same
greatest frequency, each value is used as the mode, and the data
set is said to be MULTIMODAL
- When no data value occurs more than once, the data set is said to
have NO MODE
Example:
The following data represent the duration (in days) of Space Shuttle
voyages for the years 1992-1994. (18 values)
8,9,9,14,8,8,10,7,6,9,7,8,10,14,11,8,14,11
Q: Find The Mode
Example: A manager of clothing store wants to approximate
the median age of both his male and female customers so that
he can take this into account when ordering stock. The
following data are obtained (age in years)
Female (x)
Male (y)
15
60
17
17
20
29
24
35
37
27
30
40
42
12
72
Q: Find the median age in years for both female and male customers
Example:
These data are obtained on the sales per day in thousand of
TRL at two franchises of the same hamburger chain.
Franchise A
Franchise B
0,9
2,5
1,4
2,6
0,9
0,7
4,5
0,6
1,7
3,2
3,6
1,3
0,9
4,6
0,3
5,3
2,9
3,8
2,7
5,9
1,4
3,1
5,2
4,2
3,5
0,7
4,8
4,7
2,5
5,1
1,7
5,0
A- Find the sample mean for each franchise. Based on statistics, does it appear that the
average sales per day for A is about the same as that for B? Explain.
B- Find the sample median for each franchise. Based on statistics, does it appear that the
average sales per day for A is about the same as that for B? Explain.
C- Is it safe to say the distribution of sales per day is the same for these two franchises?
Be Careful!!!! Look at the stem-and-leaf displays for the two data sets.
MONTHLY STARTING SALARY (In TRL)
Graduate
Monthly Starting
Salary
1
2,850
2
2,950
3
3,050
4
2,880
5
2,755
6
2,710
7
2,890
8
3,130
9
2,940
10
3,325
11
2,920
12
2,880
TOTAL:
35,280
A customer in a supermarket selected 6 cartons of eggs
(each containing a dozen) from a large display.
The egg-filled cartons weighed 25.9, 27.8, 25.8, 26.1, 23.5, and
45.4 ounces respectively.
a-) Find the mean weight of these cartons.
b-) Find the median weight of these cartons.
c-) Is the mean a good average in this exercise?
Five lightbulbs burned out after lasting, respectively,
for 867, 849, 840, 852, and 822 hours of
continuous use.
Find the mean and also determine what the mean
would have been if the second value had been
recorded incorrectly as 489 instead of 849.
Properties of the Mean
1- The Mean can be calculated for any set of NUMERICAL
Data
2- The Mean is unique and unambiguous value.
3- The means of several sets of data can always be
combined into the overall mean of all the data.
4- If each value in a sample were replaced by the mean, then
∑X would remain unchanged
5- The mean takes into account the value of each item in a
set of data.
6- The mean is relatively reliable in the sense that means of
many samples drawn from the same population generally do
not fluctuate, or vary, as widely as other statistics used to
estimate the mean of a population.
Properties of the Median
In addition to the properties of the Mean;
1- It splits the data into two parts
2- The median is preferable to the mean
because it is not so easily affected by extreme
values.
Problem: Imagine that four classes in Math 119 course obtained the
following mean scores on the final examination; 75, 78, 72 and 80.
Q: Could you sum these four means together and divide by 4 to obtain an
overall mean for all of the four classes?
A: This could be done only if the n (the number of students)
in each class is identical
What if;
First Class = 30 students
Second Class= 40 students
Third Class= 25 students
Fourth Class= 50 students
Then the weighted mean is =?
Problem: The following list gives the duration in minutes of 24
power failures.
18 125
44
96
31
53
26 80
49 125
63
58
45 33
89
12 103
127
75 40
80
61
129

Find the median.
28
Table: Ordered Array of Aptitude Test Scores for 40 Job Applicants. (Mean:58.45 and s:22.99)
App.
Grade
App.
Grade
App.
Grade
App.
Grade
1
20
11
42
21
56
31
78
2
21
12
43
22
58
32
80
3
23
13
43
23
59
33
81
4
25
14
46
24
61
34
85
5
30
15
48
25
62
35
90
6
35
16
50
26
65
36
92
7
36
17
51
27
68
37
96
8
39
18
52
28
70
38
98
9
40
19
54
29
71
39
99
10
41
20
55
30
75
40
100