Measures of Central Tendency, Mean, Median, Mode Disclaimer: Some parts of the presentation are obtained from various sources. Credit to the rightful owners.

1. Central Tendencies
Measurements of

2. Measurements of
Central Tendencies
A measure of central tendency is a single value that attempts to
describe a set of data by identifying the central position within
that set of data. As such, measures of central tendency are
sometimes called measures of central location. They are also
classed as summary statistics.

3. 5/5
3
3
3
33

4. 5/53
33
3
3

5. 5/5
3
4
4
45

6. 5/5
5
4
4
4
3

7. 5/5
3
2
2
21

8. 5/5
3
2
2
2
1

9. Measurements of
Central Tendencies
A measure of central tendency is defined as the statistical
measure that identifies a single value as representative of an
entire distribution.
MEAN MEDIAN MODE

10. MEAN (Arithmetic Mean)
The sum of all data divided by the total number of data.
3, 3, 3, 3, and 3
3 + 3 + 3 + 3 + 3
5
= 3
3, 4, 4, 4, and 5
3 + 4 + 4 + 4 + 5
5
= 4
3, 2, 2, 2, and 1
3 + 2 + 2 + 2 + 1
5
= 2
Arithmetic mean =
sum of all data
number of data

11. MEAN (Arithmetic Mean)
A group of canned food makers label their can as having 250
grams of net weight. When carefully inspected, ten cans are
found to have weights ranging from 248 grams to 255 grams. The
following is the list of weights of ten cans.
250, 252, 248, 251, 249, 250, 253, 255, 248, and 253
250 + 252 + 248 + 251 + 249 + 250 + 253 + 255 + 248, +253
10
2,509
10
250.9
=
=

12. Find the arithmetic mean of 1, 3, 3, 4, 4, 5, 5, 6, and 6
1 + 3 + 3 + 4 + 4 + 5 + 5 + 6 + 6
9
=
37
9
≈ 4.11

13. The average weight of group of students is 51.2 kilograms.
1) What is the total weight of ten students?
2) If another new students whose weight is 58.0 kilograms joins
the group, what will the new average weight of the students?
51.2
𝑁
10
=
𝑁 = 51.2 × 10
𝑁 = 512 kilograms
Average
512 + 58
11
= ≈ 51.82 kilograms

23. 1) The average of a list of 6 numbers is 20. If
we remove one of the numbers, the average
of the remaining numbers is 15. What is the
number that was removed?

24. 2) Timothy's average score on the first 4 tests
was 76. On the next 5 tests his average score
was 85. What was his average score on all 9
tests?

25. 3) Tracy mowed lawns for 2 hours and earned
$7.40 per hour. Then she washed windows
for 3 hours and earned $6.50 per hour. What
were Tracy's average earnings per hour for
all 5 hours?

26. 4) After taking 3 quizzes, your average is 72 out
of 100. What must your average be on the 5
quizzes to increase your average to 77?

27. 5) A class of 25 students took a science test. 10
students had an average score of 80. The
other students had an average score of 60.
What is the average score of the whole
class?

28. 6) Fifteen accounting majors have an average
grade of 90. Seven marketing majors
averaged 85, and ten finance majors
averaged 93. What is the mean for the 32
students?

29. 7) Miss Holton drives 4 hours at an average
speed of 30 miles per hour. Then she drives
2 hours at a speed of 45 miles per hour.
What is her average speed for the whole
trip?

30. • http://www.math-only-math.com/word-
problems-on-arithmetic-mean.html

31. A. Find the arithmetic mean of the weights of ten students
41, 38, 35, 40, 39, 42, 29, 45, 43, and 40
41 + 38 + 35 + 40 + 39 + 42 + 29 + 45 + 43 + 40
10
= 39.2 kilograms
B. Find the arithmetic mean of the salaries of seven office workers
9,750 7,500 8,800 10,700 24,000 6,500 8,500
9,750 + 7,500 + 8,800 + 10,700 + 24,000 + 6,500 + 8,500
7
= 10,821.43 baht

33. MEDIAN
The median of a set of data is the middlemost number in the set. The median is also
the number that is halfway into the set. To find the median, the data should first be
arranged in order from least to greatest.
B. Find the arithmetic mean of the salaries of seven office workers
9,500 7,500 8,800 10,700 24,000 6,500 8,500
9,500 + 7,500 + 8,800 + 10,700 + 24,000 + 6,500 + 8,500
7
= 10,821.43 baht
6,500 7,500 8,500 8,800 9,800 10,700 24,000
Median = 8,800 baht

34. MEDIAN
The median of a set of data is the middlemost number in the set. The median is also
the number that is halfway into the set. To find the median, the data should first be
arranged in order from least to greatest.
C. From a group of students, two are 164 centimeters tall, three are 166 centimeters tall,
two are 172 centimeters tall, and the last four are 165, 168, 169, and 175 centimeters
tall. What is the median of the heights of these students?
164 164 165 166 166 166 168 169 172 172 175
Median = 166 cm

35. B. Find the median of the salaries of seven office workers
6,500 7,500 8,500 8,800 9,800 10,700 24,000
C. From a group of students, two are 164 centimeters tall, three are 166 centimeters tall,
two are 172 centimeters tall, and the last four are 165, 168, 169, and 175 centimeters
tall. What is the median of the heights of these students?
164 164 165 166 166 166 168 169 172 172 175
D. Find the median of the data set
15 18 19 23 24 29 31 33 35 37
Median =
24 + 29
2
= 26.5

36. D. James weighed six mangoes and noted the following data: 380, 420, 395, 432, 390, and
408 grams. What is the median of the weights of these mangoes?
380 390 395 408 420 432
Median =
395 + 408
2
= 401.5 grams

42. Mode
• The most frequently occurring value in a data
set
• Applicable to all levels of data measurement
(nominal, ordinal, interval, and ratio)
• Bimodal -- Data sets that have two modes
• Multimodal -- Data sets that contain more
than two modes

43. Mode: 1 and 4
Mode: 1
Mode: 10

44. Step 1 23 = 22 + 25 + 23 + 22 + 23 + 24 + 𝑥
7
161 = 22 + 25 + 23 + 22 + 23 + 24 + 𝑥
𝑥 = 161 − 22 + 25 + 23 + 22 + 23 + 24
𝑥 = 22
Step 2 22 25 23 22 23 24 22
Mode: 22

45. http://www.kidsmathgamesonline.com/numbers/meanmedianmode.html