MODULE II
MEASURES OF CENTRAL TENDENCIES
2.1 CENTRAL TENDENCY
Central tendency is the point (or value) about which all other scores in the
distribution or data set tend to cluster. For this reason, it is often referred to as
averages. It is a single number which represents the general level of performance of a
group.
The three commonly measures of central tendencies are:
The Mean
The Median
The Mode
2.2 THE MEAN
The mean is defined as the sum of the values in the data set or distribution
divided by the number of values. It is the most commonly used measure of central
tendency. In ungrouped data, it is called arithmetic mean.
When to use the mean
1. When the frequency distribution or set of data does not contain either open
ended or extreme value.
2. When the measure of central tendency having the greatest stability is
desired.
3. When other parameters or statistics like standard deviation, variance,
coefficient of correlation, etc. are to be computed later.
4. When dealing with either interval or ratio scale of measurement.
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Calculating the Arithmetic Mean of ungrouped data
Formula :
x =
𝛴𝑥
Where: x = score
N = number of scores
Σ = summation
𝑁
Illustrative example:
Last week, a fruit vendor earned the following income from selling
fruits
at the Baclaran: Tuesday - ₱ 650, Wednesday - ₱ 900, Thursday - ₱ 720,
Friday - ₱ 610, Saturday - ₱ 780, and Sunday - ₱ 950. What is the arithmetic
mean of his income?
Solution:
Given: Σx = ₱ 650 + ₱ 900 + ₱ 720 + ₱ 610 + ₱ 780 +
₱ 950
= ₱ 4610
N = 6 (number of days)
X =
𝛴𝑥
𝑁
, x=
₱ 4,610
6
, x = 768.33
Calculating the Weighted Mean of ungrouped data.
The weighted arithmetic mean is expressed as the sum of the product
each value and its corresponding weight divided by the sum of the weights.
Formula:
X =
𝛴ƒ𝑥
𝛴ƒ
or
xw =
𝛴𝑤𝑥
𝛴𝑤
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Illustrative example:
The final grades of a student at the end of the
semester are the following:
Subject
Accounting
Human Resource Mgt.
Economics
English
Finance
Grades
(x)
2.25
2.50
1.75
1.50
2.00
Units
(ƒ)
6
3
3
3
3
What is the weighted mean grade of the student?
Solution:
Xw =
6(2.25)+ 3(2.50) + 3(1.75) + 3(1.50) + 3(2.00)
6+ 3+ 3+ 3+ 3
=
36.75
18
= 2. 04
Calculating the Mean of grouped data
Formula:
X =
𝛴ƒ𝑥
𝑛
for sample mean
µ=
𝛴ƒ𝑥
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𝑁
for population mean
Illustrative example:
Given the following scores of 50 selected tourism students who took the test in
Algebra:
47 29 31 37 34 41 36 36 36 42
36 48 30 42 39 31 34 37 44 39
43 37 35 33 34 31 30 43 38 35
31 31 35 38 45 40 38 35 32 25
40 38 35 32 22 41 38 35 33 23
n = 50
Step 1. Tabulate the data in a grouped frequency distribution and determine
the Frequency (ƒ), and the Class Mark (X). (See table below)
Step 2. Multiply the frequency and the class mark in every class and get the
sum.
Grouped Frequency Distribution of 50 selected Tourism students
who took the test in College Algebra.
48
45
42
39
36
33
30
27
24
21
ci
- 50
- 47
- 44
- 41
- 38
- 35
- 32
- 29
- 26
- 23
Tally
ƒ
1
1
11
2
11111
5
111111
6
111111111111 12
11111111111
11
111111111
9
1
1
1
1
11
2
n = 50
X
ƒX
49
49
46
92
43
215
40
240
37
444
34
374
31
279
28
28
25
25
22
44
ΣƒX = 1,790
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Step 3. Solve for the sample mean ( x ).
X =
𝛴ƒ𝑥
𝑛
=
1,790
50
= 35.84
Question: What does the sample mean of 35.84 tell you as regard to the
performance of 50 TM students in College Algebra test?
Another method for solving the sample mean of a grouped frequency
distribution is by the use of Deviation or Coded formula
X = AM +
𝛴ƒ𝑑
𝑛
(ἰ)
Where: AM = Assumed Mean (X with the highest ƒ)
ἰ = interval
ƒ = frequency
d = deviation from AM
Study the table below
Grouped Frequency Distribution of 50 selected Tourism students
who took the test in College Algebra.
48
45
42
39
36
33
30
27
24
21
ci
- 50
- 47
- 44
- 41
- 38
- 35
- 32
- 29
- 26
- 23
ƒ
1
1
11
2
11111
5
111111
6
111111111111 12
11111111111
11
111111111
9
1
1
1
1
11
2
n= 50
Tally
X
49
46
43
40
37
34
31
28
25
22
d ƒd
4
3
2
1
0
-1
-2
-3
-4
-5
Σƒd =
Solve for the sample mean using the deviation or coded formula. (Seatwork)
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2.3 THE MEDIAN
The Median (Md) is a measure of central tendency that occupies the middle
position in the frequency distribution or set of data. It is the value that divides the
distribution or data set into two, such that 50% of the data lies above the median and
the other 50% lies below it.
When to use the Median
1. When the data set or distribution is open-ended or contains extreme values.
2. When the data is arranged in descending or ascending order.
3. When the exact midpoint of the distribution is desired.
4. When dealing with ordinal data.
Calculating the Median of ungrouped data
A. When N is even, the median value is obtained using the formula:
Md =
𝑀𝑉1 + 𝑀𝑉2
2
Illustrative example:
Ten middle-management employees of a certain company have the
following ages:
52, 45, 49, 48, 53, 42, 50, 53, 55, 58.
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Find the median age.
Arrange the data in ascending order:
42, 45, 48, 49, 50, 52, 53, 53, 55, 58
n = 10 (even number)
Solution:
Md =
𝑀𝑉1 + 𝑀𝑉2
2
=
50 + 52
2
= 51
B. When N is odd, the median is the value exactly at the middle of the data set
arranged either in descending or ascending order.
Illustrative example:
The daily rates of a sample of nine employees of RomAn firm are:
₱ 520, ₱ 450, ₱ 560, ₱ 500, ₱ 720, ₱ 660, ₱ 840, ₱ 490, ₱ 870
What is the median daily rate?
Arrange the data set in descending order
₱ 870, ₱ 840, ₱ 720, ₱ 660, ₱ 560, ₱ 520, ₱ 500, ₱ 490, ₱ 450
n = 9 (odd number)
Solution:
The median daily rate is the middle value ₱ 560 .
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Calculating the Median of grouped data
Frequency distribution of 50 selected TM students
who took the test in Algebra
ci
𝑓
48 - 50
1
45 - 47
2
˃ c𝑓
47.5 – 50.5
˂
c𝑓
50
44.5 - 47.5
49
3
41.5 - 44.5
47
8
38.5 - 41.5
42
14
35.5 - 38.5
36
26
32.5 - 35.5
24
37
29.5 - 32.5
13
46
26.5 - 29.5
4
47
23.5 - 26.5
3
48
20.5 - 23.5
2
50
X
CB
1
49
𝑓AMd class
46
AMd class
42 - 44
5
c𝑓p
43
39 - 41
6
40
36 - 38
12
37
33 - 35
11
n = 50
34
30 - 32
9
31
27 - 29
1
28
24 - 26
1
25
21 - 23
2
22
Formula:
𝑛
−𝑐𝑓𝑝
2
Md = LB + 〔 𝑓(𝐴𝑀𝑑)
〕ἰ ,
Where: LB
C𝑓p (AMd) ἰ -
Lower class boundary
the ˂ c𝑓 preceding the ˂ c𝑓 of the AMd class
frequency of the AMd class
interval
Solution:
Step 1. Find the AMd class applying
1
2
(𝑛) =
1
2
(50) = 25.
Counting from ˂ c𝑓 of the lowest class and moving upward
(arrow), 25 falls on ˂ c𝑓 36. Therefore, AMd class is
〔36 – 38〕.
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Step 2. Write the values of the following variables with respect to
the AMd :
𝑓AMd class = 12
LB = 35.5
ἰ = 3
C𝑓p = 24
Step 3. Substitute the formula and solve for the Md.
Md = LB + 〔
1
(𝑛)−𝑐𝑓𝑝
2
𝑓𝐴𝑀𝑑
1
〕 ἰ = 35.5 + 〔
1
(50)−24
2
12
〕3
= 35.5 +〔0.08 〕3
Md = 35.5 + 〔 12 〕 3
= 35.5 + 0.24
Md = 35.74
For purposes of checking this solution, the ˃ c𝑓 is used in the formula:
1
Md = UB - 〔 2
(𝑛)−𝑐𝑓𝑝
𝑓𝑀𝑑
〕ἰ
2.4 THE MODE
The Mode (Mo) is that single data or score which occurs most frequently in a
data set. In grouped frequency distribution, the Mode (called crude mode) is the
midpoint with the highest frequency.
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When to use the Mode
1. When a quick and approximate measure of central tendency is desired
2. When the data is either quantitative or qualitative.
3. When the frequency distribution contains open-ended or extreme values.
4. When dealing with nominal data.
Calculating the Mode of ungrouped data
Data set may have no mode. If it contains one mode, it is called
Unimodal. If there are two modes, it is called Bimodal, three modes or
Trimodal.
Illustrative examples:
1. The following data represent the total unit sales for MYRO
2000from a sample of 10 Gaming Centers for the month of October:
16, 18, 11, 13, 14, 11, 15, 11, 6, 7.
Find the mode.
Arrange the data in ascending or descending order.
6, 7, 11, 11, 11, 13, 14, 15, 16, and 18.
The Mode is 11. Unimodal.
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2. An operation manager in charge of a company’s manufacturing
keeps track of the number of manufactured LCD television in a day. If the
number of LCD”s produced in the past 3 weeks were:
21, 19, 20, 26, 21, 22, 21, 26, 31, 30, 29, 30, 26, 26, 28, 27, 23, 21.
What is the mode of these data?
Arranging the data,
19, 20, 21, 21, 21, 21, 22, 23, 26, 26, 26, 26, 27, 28, 29, 30, 30, 31
There are two modes, 21 and 26. Bimodal
3. Nine middle-management of a certain company have the following
ages:
47, 52, 59, 56, 55, 49, 60, 46, 54.
What is the mode of this data set?
None.
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Calculating the Mode of grouped data
Grouped Frequency Distribution of 50 selected Tourism
students who took the test in College Algebra.
48
45
42
39
36
33
30
27
24
21
ci
-
f
1
2
5
6
12
11
9
1
1
2
50
47
44
41
38
35
32
29
26
23
CB
47.5 – 50.5
44.5 – 47.5
41.5 – 44.5
38.5 – 41.5
35.5 – 38.5
32.5 – 35.5
29.5 – 32.5
26.5 – 29.5
23.5 – 26.5
20.5 – 23.5
Find the Mode of this distribution using the formula:
Mo = LB +
𝑑1
ἰ,
𝑑1+𝑑2
Where: LB = Lower boundary of the modal class
The modal class is the class with the highest frequency.
d1 = Difference between the frequency of the modal class and the
frequency of the class immediately below it.
d2 = Difference between the frequency of the
modal class and the frequency of the class above it.
Given:
Modal Class = (36 - 38)
LB = 35.5
d1 = 12 – 11 = 1
d2 = 12 - 6 = 6
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Solution:
𝑑1
Mo = LB + 〔 𝑑1 +
〕ἰ
𝑑2
Mo = 35.5 + (0.14) 3
1
= 35.5 + 〔 1+6 〕 3
= 35.5 + 0.42
Mo = 35.92
2.5 MEASURES OF LOCATION OR QUANTILES
Quantiles are measures of position which divide the data set or frequency
distribution into equal parts. They are the natural extension of the Median. While the
median divides the distribution or data set into two parts, quantiles divide it into four,
ten, and 100 equal parts.
2.6 THE QUARTILES
Quartiles are quantiles that divide the data set or frequency distribution
into four equal parts, such that 25 % of the data falls below the first quartile (Q1), 50
% of the data falls below second quartile (Q2), and 75 % of the data falls below the
third quartile (Q3). Q1, Q2, and Q3 are the score – points which divides the set or
distribution into four parts.
Calculating the Quartiles of ungrouped data
The general formula of Quartiles for ungrouped data
Qk =
𝒌 (𝑵+𝟏)
𝟒
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Illustrative example:
The following data give the average number of minutes required to
complete an assembly job by the 14 workers of a manufacturing plant:
79, 87, 65, 56, 64, 80, 82, 50, 65, 81, 71, 57, 65, 80
1. Solve for the values of Q1, Q2, and Q3.
2. If Michelle can finish an assembly job in 65 minutes, where does
she lie in relation to the three quartiles?
Solutions:
1. Rank the given data in ascending order and calculate the Q1, Q2 (or
Median), and Q3.
50 56 57 64 65 65 65
(even number)
Q1 = 64
Q2 =
65+71
2
71 79 80 80 81 82 87
Q3 = 80
Q2 = 68
Check the answers using the formula.
a. Q1 =
1 (14 +1)
4
=
15
4
= 3.75th. or the 4th. value which is 64
Q1 = 64
b. Q2 =
2(14 +1)
4
=
30
4
= 7.5th. value or 68
Q2 = 68
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c. Q3 =
3 ( 14 +1)
4
=
45
4
= 11.25th. or the 11th. value, which is
Q3 = 80
2. Michelle’s minute falls within the first 50% below the second
quartile (Q2) (or Md) but above the first quartile (Q1)
2.7 THE DECILES
Deciles are quantiles that divide the data set or distribution into ten
equal parts. There are nine score – points, denoted by D1, D2, D3. . . , D9.
Calculating the Deciles of ungrouped data
The general formula is
Dk =
𝒌 (𝑵+𝟏)
𝟏𝟎
Illustrative example:
A newly open supermarket conducted a survey to determine the
age of customers that patronize the store on a given Sunday. A random
sample of 24 customers was interviewed and the following ages were
obtained:
47, 28, 19, 16, 41, 36, 25, 32, 18, 19, 35, 35, 21, 39, 26, 45, 22, 31, 42,
27, 40, 26, 9, 12.
Find D3, D6, and D8
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Solution:
Arrange the data in ascending order.
9, 12, 16, 18, 19, 19, 21, 22, 25, 26, 26, 27, 28, 31, 32, 35, 35, 36, 39,
40, 41, 42, 45, 47
D3 = 21.5
D5 = 27.50 D6= 32
D8 =
40
3 (24 +1)
1. D3 =
10
=
75
10
= 7.5th. value = 21.5
It means that 30% of the values in the data set falls below 21.5.
2. D6 =
6 (24+1)
10
=
150
10
= 15th. value = 32
60% of the values is less than 32.
3. D8 =
8 (24+1)
10
=
200
10
= 20th. value = 40
Supply your own description.
2.8 THE PERCENTILES
Percentiles are score – points that divide the set or distribution into
one hundred equal parts. It is used to assess performance by determining the
position of one score relative to others.
Percentile Rank (PR) is a percentage. It tells what percent of the cases
got below the rank position. It is computed when the percentile is given.
Percentile Point (Pn) is the score or value that corresponds to the
given percentile rank.
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Calculating the percentiles of ungrouped data
The formula is:
Pk =
𝑘(𝑁+1)
100
Illustrative example:
A class of 20 BSBA students were given 30-item quiz in Statistics. The
scores obtained are the following:
26, 29, 30, 5, 19, 23, 15, 17, 24, 9, 12, 11, 10, 7, 10, 14, 9, 10, 8, 5.
1. Solve for the P25, P50, and P75.
2. If Eunice Milca got a score of 26 and is ranked 3rd. in the class, how
many students are ranked below her?
3. What percent of the students ranked below her?
4. What are the percentile rank and percentile point of Eunice?
5. What percent of the students ranked above her?
Solutions:
Arranging the data in ascending order.
3, 5, 7, 8, 9, 9, 10, 10, 10, 11, 12, 14, 15, 17, 19, 23, 24, 26, 29,30.
1. Solving for P25, P50, P75.
P25 =
25(20+1)
100
=
525
100
= 5.25th. value = 9
This means that 25% of the scores falls below 9. It can also means that
25% of the students got a score below 9.
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P50 =
50( 20+1)
100
=
1,050
100
= 10.5th. value = 11.5
Provide your own description here.
P75 =
75(20+1)
100
=
1,575
100
= 15.75th. value = 22
Provide your own description here.
2. The number of students ranked below Eunice Milca:
20 – 3 = 17 (17 students got scores below her)
3. The percent of students ranked below her:
%=
𝑁𝑜.𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠 𝑤𝑖𝑡ℎ 𝑠𝑐𝑜𝑟𝑒 𝑏𝑒𝑙𝑜𝑤 26
𝑁𝑜.𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑐𝑙𝑎𝑠𝑠
4. Percentile rank =
17+1
20
x 100% = 90 %
Percentile point = 26
5. Percent of students ranked above Eunice
% =
2
20
x 100% = 10%
Calculating the Quartiles of grouped data
Formula:
Qk = LB + 〔
𝑘
(𝑛
4
) −𝑐𝑓𝑝
𝑓𝐴𝑄1
17
x 100% = 20 x 100% = 85 %
〕ἰ
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The procedure for solving problems on quantiles is similar to the median (Md)
because, as mentioned earlier, quantiles are natural extensions of the median.
Illustrative example:
The following is a distribution of the number of employees in 50 companies
belonging to a certain service business:
Number of Employees
ci
69 - 76
61 - 68
53 - 60
45 - 52
37 - 44
29 - 36
21 - 28
No. of Companies
𝑓
6
8
10
13
7
4
2
n = 50
CB
69.5 - 76.5
60.5 - 68.5
52.5 - 60.5
44.5 - 52.5
36.5 - 44.5
28.5 - 36.5
20.5 - 28.5
Solving for the first quartile (Q1)
Solution:
Step 1. Assumed Q1 class:
1
4
1
(𝑛) = 4 (50) = 12.5.
Step 2. AQ1 class = (37 - 44)
c𝑓p = 6
𝑓AQ1 class = 7
LB = 36.5
ἰ = 8
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˂ c𝑓
50
44
36
26
13
6
2
˃ 𝑓c
6
14
24
37
44
48
50
Step 3. Substitution:
1
Q1 = LB +〔 4
Q1 = 36.5 + 〔
(𝑛) −𝑐𝑓𝑝
𝑓𝐴𝑄1
12.5 − 6
7
1
〕ἰ
〕8
(50) −13
= 36.5 + 〔 4
= 36.5 + 〔
6.5
13
〕8
7
〕8
= 36.5 + 7.43
Q1 = 43.95 〔 It falls within the ci = (37 – 44)〕
This means that 25 % of the data in the distribution falls below 43.95.
Solving for the third quartile (Q3)
Solution:
Assumed Q3 class:
3
4
(𝑛) =
3
4
(50) = 37.5 (61 – 68)
c𝑓p = 36
LB = 60.5
𝑓AQ3 = 8
ἰ= 8
3
Q3 = LB + 〔4
Q3 = 60.5 + 〔
(𝑛) − 𝑐𝑓𝑝
𝑓𝐴𝑄3
37.5 −36
8
3
〕ἰ
= 60.5 + 〔 4
〕8
= 60.5 + 〔
(50) −36
1.5
8
8
〕8
Q3 = 62.00 (Give your own description.)
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〕8
= 60.5 + 1.5
Calculating the Deciles of grouped data
Formula:
𝑘
Dk = LB + 〔 10
( 𝑛) −𝑐𝑓𝑝
𝑓𝐴𝐷𝑘
〕ἰ
A class of 60 BSHRM students was given a test in Accounting and the following scores are
arranged in the distribution, as shown below:
Class Interval Frequency
(c i)
(𝑓)
52
47
42
37
32
27
22
17
12
-
56
51
46
41
36
31
26
21
16
3
5
8
10
13
9
6
4
2
N = 60
Class Boundary
(CB)
51.5
46.5
41.5
36.5
31.5
26.5
21.5
16.5
11.5
-
56.5
51.5
46.5
41.5
36.5
31.5
26.5
21.5
16.5
Cumulative
Freq.
˂ c𝑓
60
57
52
44
34
21
12
6
2
Determine the :
(1)
Fourth Decile (D4)
(2)
Seventh Decile (D7).
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Cumulative
Freq.
˃ c𝑓
3
8
16
26
39
48
54
58
60
Solutions:
(1) Fourth Decile (D4)
4
Assumed D4 class:
10
(𝑁) =
4
10
(60) = 24 〔32 - 36 〕
c𝑓p = 21
𝑓AD4 = 13
ἰ = 5
LB = 31.5
D4 = LB + 〔
4
10
(𝑁) −𝑐𝑓𝑝
𝑓𝐴𝐷4
〕ἰ
24 − 21
D4 = 31.5 + 〔
13
= 31.5 + 〔
4
(60) −21
10
〕5 =
13
3
〕5
= 31.5 + 〔 〕 5
13
= 31.5 + 1.15
D4 = 32. 65
Means that 40 % of the scores or data in the distribution is less than 32.65
(2) Seventh Decile (D7)
7
Assume D7 Class: 10 (𝑁) =
7
10
(60) = 42 (37 - 41)
c𝑓p = 34
𝑓AD7 = 10
LB = 36.5
ἰ = 5
7
D7 = LB + 〔 10
D7 = 36.5 + 〔
(𝑁) − 𝑐𝑓𝑝
𝑓𝐴𝐷7
42 − 34
10
7
〕ἰ
=
36.5 + 〔 10
〕5
=
36.5 + 〔 10 〕 5
8
D7 = 40.50
(Make your own description.)
ISHRM 2014
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Statistics
MT 312/MT 322/TM Module II
(60) −34
10
〕 5
= 36.5 + 4
Calculating the Percentiles of grouped data
Formula:
𝑘
− 𝑐𝑓𝑝
Pk = LB + 〔100𝑓𝐴𝑃𝑘 〕 ἰ
Frequency distribution of scores of 60 BSHRM students in Statistics test.
Class Interval Frequency
(c i)
(𝑓)
52
47
42
37
32
27
22
17
12
-
56
51
46
41
36
31
26
21
16
3
5
8
10
13
9
6
4
2
N = 60
Class Boundary
(CB)
51.5
46.5
41.5
36.5
31.5
26.5
21.5
16.5
11.5
-
Cumulative
Freq.
˂ c𝑓
60
57
52
44
34
21
12
6
2
56.5
51.5
46.5
41.5
36.5
31.5
26.5
21.5
16.5
Cumulative
Freq.
˃ c𝑓
3
8
16
26
39
48
54
58
60
Solve for the:
( 1 ) Thirtieth Percentile (P30)
( 2 ) Seventieth Percentile (P70)
Solutions:
(1) Thirtieth Percentile (P30)
30
Assumed P30 class: 100 (𝑁) =
30
100
(60) = 18 〔27 - 31〕
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Statistics
MT 312/MT 322/TM Module II
Cfp = 12
ƒAP30 = 9
LB = 26.5
ἰ = 5
P30 = LB + [
30
(12)−𝑐𝑓𝑝
100
〕ἰ
𝑓𝐴𝑃30
P30 = 26.5 + 〔
18 − 12
9
= 26.5 + 〔
30
( 60) −
100
6
= 26.5 + 〔 9 〕 5
〕 5
12
9
〕5
= 26.5 + 3.33
P30 = 29.83
Write your description here.
(2) Seventieth Percentile (P70)
70
Assumed P70 class: 100 (𝑁) =
70
100
(60) = 42 (37 – 41)
cƒp = 34
ƒAP70 = 10
LB = 36.5
ἰ = 5
𝑘
(𝑁) −𝑐𝑓𝑝
P70 = LB + [ 100𝑓𝐴𝑃70
P70 = 36.5 + 〔
42 − 34
10
70
]ἰ
〕5
= 36.5 + 〔 100
8
= 36.5 + 〔 10 〕 5
P70 = 40.50
Write your description here.
ISHRM 2014
Learning Material
Statistics
MT 312/MT 322/TM Module II
(60) − 34
10
〕5
= 36.5 + 4.0
WORK PROJECT / LEARNING ACTIVITY 1, MODULE 2
Name: _____________________________ Yr/Sec: ____________ Date:
__________________
A. IDENTIFICATION.
_______________________ 1. It is the point (or value) about which all other scores
in the distribution or data set tend to cluster.
_______________________ 2. It is defined as the sum of the values in the data set or
distribution divided by the number of values.
________________________ 3. It is expressed as the sum of the product of each value
and its corresponding weight divided by the sum of the
weights.
________________________ 4. This refers to the measure of central tendency that
occupies the middle position in the frequency
distribution or set of data.
________________________ 5. It is that single data or score which occurs most
frequently in a data set.
________________________ 6. These are measures of position which divide the data
set or frequency distribution into equal parts.
________________________ 7. These quantiles divide the data set or frequency
distribution into four equal parts.
________________________ 8. The quantiles that divide the data set or distribution
into ten equal parts and consists of nine score – points.
________________________ 9. These are score – points that divide the set or
distribution into one hundred equal parts.
________________________ 10. It tells what percent of the cases got below the rank
position. It is computed when the percentile is given.
ISHRM 2014
Learning Material
Statistics
MT 312/MT 322/TM Module II
WORK PROJECT / LEARNING ACTIVITY 2, MODULE 2
Name: _____________________________ Yr/Sec: ____________ Date:
__________________
B. MULTIPLE CHOICE.
__________ 1. The score or value that corresponds to the given percentile rank is
termed
a. Percentile
c. Percentile Point
b. Percentile Rank
d. None
__________ 2. Which of the following is a percentage?
a. Percentile Point
c. Percentile
b. Percentile Rank
d. None
__________ 3. The following are all measures of central tendencies, except
a. Mode
c. Median
b. Mean
d. Quartile
__________ 4. The measures of central tendencies are also called
a. Quantiles
c. Centiles
b. Measures of position
d. Averages
__________ 5. The following are all measures of position, except
a. Decile
c. Median
b. Quartile
d. Percentile
ISHRM 2014
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Statistics
MT 312/MT 322/TM Module II
__________ 6. Which central tendency measures the level of performance of a group?
a. Quartile
c. Decile
b. Percentile
d. Mean
__________ 7. The most commonly used measure of central tendency is the
a. Mode
c. Percentile
b. Mean
d. Median
__________ 8. The measure of central tendency which divides a data set or frequency
distribution into two parts, such that 50% of the data lies below it and the
other 50% lies above it, is referred to as
a. Weighted Mean
c. Arithmetic Mean
b. Sample Mean
d. None
__________ 9. The midpoint with the highest frequency in the data set or frequency
distribution is referred to as
a. Quartile
c. Mode
b. Percentile
d. Median
__________ 10. The following are all natural extensions of the Median, except
a. Quatiles
c. Deciles
b. Percentiles
d. None
ISHRM 2014
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Statistics
MT 312/MT 322/TM Module II
__________ 11. These are score-points that divide a data set or frequency distribution
into 25 %, 50 %, and 75 %.
a. Quatiles
c. Deciles
b. Percentiles
d. None
__________ 12. Which of the following measures of position is used to assess
performance by determining the position of one score relative to the
others?
a. Percentile
b. Decile
c. Quartile
d. None
__________ 13. It is used when other parameters or statistics like standard deviation,
variance, coefficient of correlation, etc. are to be computed later.
a. Quartile
c. Percentile
b. Median
d. Mean
__________ 14. Which of the following is affected by open ended or extreme value on
either or both ends of the distribution?
a. Mean
c. Median
b. Quartile
d. Mode
___________ 15. It is used when a quick and approximate measure of central tendency
is desired.
a. Mean
c. Quartile
b. Median
d. Mode
ISHRM 2014
Learning Material
Statistics
MT 312/MT 322/TM Module II
WORK PROJECT / LEARNING ACTIVITY 3, MODULE 2
Name: _____________________________ Yr/Sec: ____________ Date:
__________________
C. PROBLEM SOLVING.
1. A researcher wished to study the trend in the attendance of the employees at a
certain five-star hotel. 60 employees were selected at random and a record was consulted to
determine the number of absences these employees incurred for a certain month. The
following is a frequency distribution on the number of absences of the employees.
No. of Absences
(c ἰ)
0–2
3–5
6–8
9 – 11
12 – 14
15 - 17
18 – 20
21 – 13
24 – 26
No. of Employees
(ƒ)
3
5
8
11
14
17
20
23
26
n = 60
Complete the table with the required variables and solve for the following:
a. Mean
a.1 If Michelle, an employee, has 7 absences and is rank 8, what percent
of the employees incurred absences more than her?
a.2 What is Michelle’s level of performance in terms of the attendance
record of the hotel?
ISHRM 2014
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Statistics
MT 312/MT 322/TM Module II
b. Median
c. Mode
2. The service time in minutes for 15 customers at a reservation counter is given
below.
2, 1, 7, 8, 3, 5, 10, 15, 12, 13, 9, 5, 5, 9, 2
Rearrange the data set in ascending order and solve for the following:
a. Arithmetic Mean
b. Median
c. Mode
3. The average family income (in thousand pesos) in 2013 for each of the 13 regions
in the Philippines was
59, 24, 25, 28, 29, 30, 22, 21, 25, 39, 28, 19, 32
Rank the data set in ascending order and solve for the following:
a. Q1, Q2, and Q3 and rank the data set according to these three quartiles.
b.
D2.5,
D5, and D7.5 and rank the set according to these three deciles.
c. P25, P50, and P75 and rank the set according to these three percentiles.
d. What do you observed? Explain your observation.
ISHRM 2014
Learning Material
Statistics
MT 312/MT 322/TM Module II
4. A BSHRM class of 50 students was given a test in Accounting, and the data obtained were
arranged in a frequency distribution, as shown below
Score
(c ἰ )
37 - 41
32 - 36
27 - 31
22 - 26
17 - 21
12 - 16
7 - 11
No. of students
(ƒ)
5
7
9
10
8
7
4
N = 50
˂ c𝑓
5
12
21
31
39
46
50
Determine the following:
a. Q1, Q2, and Q3
b. D4 and D8
c. P20 and P70
c.1 If Lourdes got a score of 33 and is ranked 9, what percent of the students
got a score below 33? What percent of students got a score above 33
c.2 What is the percentile rank of Lourdes?
ISHRM 2014
Learning Material
Statistics
MT 312/MT 322/TM Module II