This document defines and provides examples for calculating measures of central tendency (mean, median, mode) and dispersion (range) from datasets. It explains that the mean is the average found by adding all values and dividing by the number of items, the median is the middle number, and the mode is the most frequent value. The range is defined as the difference between the highest and lowest values. Step-by-step instructions and examples are given for calculating each measure from sets of numbers.

1. Mean, Median, Mode
& Range
Prof.Dr.Chinna Chadayan.N
Professor,
Enam Nursing College
Descriptive
Statistics

2. Copyright © 2000 by Monica Yuskaitis
Definition
Mean
Means
Average

3. Mean
• Mean:
–A measure of center, also known as
average.
–Mean is the sum of a set of data
divided by the number of data
items.

4. Copyright © 2000 by Monica Yuskaitis
Definition
• Mean – the average of a
group of numbers.
2, 5, 2, 1, 5
Mean = 3

5. Copyright © 2000 by Monica Yuskaitis
Mean is found by evening out
the numbers
2, 5, 2, 1, 5

6. Copyright © 2000 by Monica Yuskaitis
Mean is found by evening out
the numbers
2, 5, 2, 1, 5

7. Copyright © 2000 by Monica Yuskaitis
Mean is found by evening out
the numbers
2, 5, 2, 1, 5
mean = 3

8. Copyright © 2000 by Monica Yuskaitis
How to Find the Mean of a
Group of Numbers
• Step 1 – Add all the numbers.
8, 10, 12, 18, 22, 26
8+10+12+18+22+26 = 96

9. Copyright © 2000 by Monica Yuskaitis
How to Find the Mean of a
Group of Numbers
• Step 2 – Divide the sum by
the number of addends.
8, 10, 12, 18, 22, 26
8+10+12+18+22+26 = 96
How many addends are there?

10. Copyright © 2000 by Monica Yuskaitis
How to Find the Mean of a
Group of Numbers
• Step 2 – Divide the sum by
the number of addends.
6)96 sum
# of addends
1
6
36
6
6
3

11. Copyright © 2000 by Monica Yuskaitis
How to Find the Mean of a
Group of Numbers
The mean or average of these
numbers is 16.
8, 10, 12, 18, 22, 26

12. Copyright © 2000 by Monica Yuskaitis
What is the mean of these
numbers?
7, 10, 16
11

13. Copyright © 2000 by Monica Yuskaitis
What is the mean of these
numbers?
2, 9, 14, 27
13

14. Copyright © 2000 by Monica Yuskaitis
What is the mean of these
numbers?
1, 2, 7, 11, 19
8

15. Copyright © 2000 by Monica Yuskaitis
What is the mean of these
numbers?
26, 33, 41, 52
38

16. Copyright © 2000 by Monica Yuskaitis
Definition
Median
is in the
Middle

17. Median
• Median:
– A measure of center, that tells the middle number
in a set of data.
– If there is no single middle item, the number
halfway between the two data items closest to the
middle is the median.
• Basically…just find the mean of the two middle
numbers.

18. Copyright © 2000 by Monica Yuskaitis
Definition
• Median – the middle number
in a set of ordered numbers.
1, 3, 7, 10, 13
Median = 7

19. Copyright © 2000 by Monica Yuskaitis
How to Find the Median in a
Group of Numbers
• Step 1 – Arrange the numbers
in order from least to greatest.
21, 18, 24, 19, 27
18, 19, 21, 24, 27

20. Copyright © 2000 by Monica Yuskaitis
How to Find the Median in a
Group of Numbers
• Step 2 – Find the middle
number.
21, 18, 24, 19, 27
18, 19, 21, 24, 27

21. Copyright © 2000 by Monica Yuskaitis
How to Find the Median in a
Group of Numbers
• Step 2 – Find the middle
number.
18, 19, 21, 24, 27
This is your median number.

22. Copyright © 2000 by Monica Yuskaitis
How to Find the Median in a
Group of Numbers
• Step 3 – If there are two middle
numbers, find the mean of these
two numbers.
18, 19, 21, 25, 27, 28

23. Copyright © 2000 by Monica Yuskaitis
How to Find the Median in a
Group of Numbers
• Step 3 – If there are two middle
numbers, find the mean of these
two numbers.
21+ 25 = 46
2)46
23 median

24. Copyright © 2000 by Monica Yuskaitis
What is the median of these
numbers?
16, 10, 7
10
7, 10, 16

25. Copyright © 2000 by Monica Yuskaitis
What is the median of these
numbers?
29, 8, 4, 11, 19
11
4, 8, 11, 19, 29

26. Copyright © 2000 by Monica Yuskaitis
What is the median of these
numbers?
31, 7, 2, 12, 14, 19
13
2, 7, 12, 14, 19, 31
12 + 14 = 26 2) 26

27. Copyright © 2000 by Monica Yuskaitis
What is the median of these
numbers?
53, 5, 81, 67, 25, 78
60
53 + 67 = 120 2) 120
5, 25, 53, 67, 78, 81

28. Copyright © 2000 by Monica Yuskaitis
Definition
Mode
is the most
Popular

29. Mode
• Mode:
– A measure of center for a set of data that tells the
item(s) that appear most often in data set.
– There can be no mode.
– There can also be more than one mode

30. Copyright © 2000 by Monica Yuskaitis
Definition
• A la mode – the most
popular or that which is in
fashion.
Baseball caps are a la mode today.

31. Copyright © 2000 by Monica Yuskaitis
Definition
• Mode – the number that
appears most frequently in a
set of numbers.
1, 1, 3, 7, 10, 13
Mode = 1

32. Copyright © 2000 by Monica Yuskaitis
How to Find the Mode in a
Group of Numbers
• Step 1 – Arrange the numbers
in order from least to greatest.
21, 18, 24, 19, 18
18, 18, 19, 21, 24

33. Copyright © 2000 by Monica Yuskaitis
How to Find the Mode in a
Group of Numbers
• Step 2 – Find the number that
is repeated the most.
21, 18, 24, 19, 18
18, 18, 19, 21, 24

34. Copyright © 2000 by Monica Yuskaitis
Which number is the mode?
29, 8, 4, 8, 19
8
4, 8, 8, 19, 29

35. Copyright © 2000 by Monica Yuskaitis
Which number is the mode?
1, 2, 2, 9, 9, 4, 9, 10
9
1, 2, 2, 4, 9, 9, 9, 10

36. Copyright © 2000 by Monica Yuskaitis
Which number is the mode?
22, 21, 27, 31, 21, 32
21
21, 21, 22, 27, 31, 32

37. Copyright © 2000 by Monica Yuskaitis
Definition
Range
is the distance
Between

38. Range
• Range:
– A measure of spread.
– The difference (subtraction) between the
greatest data value and least value in a data set.

39. Copyright © 2000 by Monica Yuskaitis
Definition
• Range – the difference between
the greatest and the least value
in a set of numbers.
1, 1, 3, 7, 10, 13
Range = 12

40. Copyright © 2000 by Monica Yuskaitis
How to Find the Range in a
Group of Numbers
• Step 1 – Arrange the numbers
in order from least to greatest.
21, 18, 24, 19, 27
18, 19, 21, 24, 27

41. Copyright © 2000 by Monica Yuskaitis
How to Find the Range in a
Group of Numbers
• Step 2 – Find the lowest and
highest numbers.
21, 18, 24, 19, 27
18, 19, 21, 24, 27

42. Copyright © 2000 by Monica Yuskaitis
How to Find the Range in a
Group of Numbers
• Step 3 – Find the difference
between these 2 numbers.
18, 19, 21, 24, 27
27 – 18 = 9
The range is 9

43. Copyright © 2000 by Monica Yuskaitis
What is the range?
29, 8, 4, 8, 19
29 – 4 = 25
4, 8, 8, 19, 29

44. Copyright © 2000 by Monica Yuskaitis
What is the range?
22, 21, 27, 31, 21, 32
32 – 21 = 11
21, 21, 22, 27, 31, 32

45. Copyright © 2000 by Monica Yuskaitis
What is the range?
31, 8, 3, 11, 19
31 – 3 = 28
3, 8, 11, 19, 31

46. Copyright © 2000 by Monica Yuskaitis
What is the range?
23, 7, 9, 41, 19
41 – 7 = 34
7, 9, 23, 19, 41

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