Q4.Week1.MATH 10
Dear God,
May we, through your
blessings,
add purity to the world,
subract evil from our lives,
multiply Your good news,
And divide Your gifts and
share them with others.
What color are you today, and
Why?
Your score
in the test
is above
average.
The average Filipino
woman is 149.60 cm
( 4 feet 10.89 inches
tall.
Stephen Curry has
averaged 36.9
points per game.
find the mean, median, and mode of
statistical data
describe the data using information from
the mean, median and mode
compare the mean, median and mode of
ungrouped data
A measure of central tendency is a single, central
value that summarizes a set of numerical data. It
attempts to describe what is “typical” in a set of data.
It is more popularly referred to as the AVERAGE.
With the average
shoe size of
Filipinas pegged
at Size 6.
Women in the
Philippines have an
average of 3 children.
1. Mean or Arithmetic Mean
– “Center of gravity” such that the “weight” of the scores
above the mean exactly balances the “weight” of the
scores below the mean
– is the sum of the data divided by the number of data
Mean (𝑿) =
𝒔𝒖𝒎 𝒐𝒇 𝒅𝒂𝒕𝒂
𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒅𝒂𝒕𝒂
=
𝑿
𝒏
Wilma Jamella Merica
4
3
3
Althea Muzza Novy Dane
4
5
4
3.5
Solutions: Find the mean amount of time the students spend
studying and doing school project.
Mean no. of hours: 𝑋 =
𝑥
𝑛
=
4+3+3+4+5+4+3.5
7
=
26.5
7
=
3.8
⸫The mean amount of time the students spend studying and
doing school project each day is 3.8 hours.
Advantages:
• Most popular measure in fields such as business,
engineering and computer science.
• It is unique - there is only one answer.
• Useful when comparing sets of data.
• Stable from group to group
Disadvantages:
• Affected by extreme values (outliers)
• Not appropriate for skewed distribution as it is
affected by extreme scores or outliers
2. Median
- The number that lies at the midpoint of the distribution of
scores; divides the distribution into two equal halves
- Is the middle number of the set of data when the data are
arranged in numerical order.
- It is the value of the
𝑛+1 th
( )
2
item or position.
Median (𝑿) =
𝑛+1 th
( )
2
Wilma Jamella Merica Althea Muzza Novy Dane
4
3
3
4
5
4
3.5
Solutions: Arrange the scores in ascending(or descending)
order.
3, 3, 3.5, 4, 4, 4, 5
There are 7 students, since 7 is an odd number, simply get the
middle score.
7+1 th
Middle position = ( ) = 4𝑡ℎ 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛
2
3, 3, 3.5, 4, 4, 4, 5
This is the median.
Advantages:
• Useful when comparing sets of data.
• More stable from group to group than the mode.
• Appropriate for skewed distributions as it is not
affected by extreme scores or outliners
Disadvantages:
• Not as popular as mean.
• Not necessarily representative
3. Mode:
– Is that number that occurs most frequently in the data.
Mode (𝑿) = 𝑚𝑜𝑠𝑡𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑡𝑙𝑦 𝑖𝑛 𝑡ℎ𝑒𝑑𝑎𝑡𝑎
Wilma Jamella Merica
4
3
3
Althea Muzza Novy Dane
4
5
4
3.5
Solutions: Arrange the scores in ascending(or descending)
order.
3, 3, 3.5, 4, 4, 4, 5
3, 3, 3.5, 4, 4, 4, 5
The mode is 4 since it
occurs most frequently.
Advantages
• Extreme values (outliers) do not affect the mode.
• Can be used for non-numerical data; colors, etc.
Disadvantages
• Not as popular as mean and median
• Not necessarily unique - may be more than one answer
• When no values repeat in the data set, the mode is every value
and is useless.
• When there is more than one mode, it is difficult to interpret
and/or compare.
If we replace the lowest grade with a zero:
Data
Original
6, 7, 8, 10, 12, 14, 14, 15, 16,
Data Set:
20
Add 3 to
9, 10, 11, 13, 15, 17, 17, 18, 19,
each data
23
value
Multiply 2
12, 14, 16, 20, 24, 28, 28, 30,
times each
32, 40
data value
Mean
Mode
Median
12.2
14
13
15.2
17
16
24.4
28
26
a) Skewed left, negatively skewed median > mean
b) Skewed right, positively skewed mean>median
c) Symmetric, mean=median=mode
Solutions: You will need to organize the data.
5, 5, 10, 10, 10, 15, 15, 15, 20, 25
Mean : 𝑋 =
𝑥
𝑛
=
2 5 +3 10 +3 15 +20+25
10
130
=
10
= 13
Median: 5, 5, 10, 10, 10, 15, 15, 15, 20, 25 Listing the data in
order is the easiest way to find the median. The numbers 10 and
15 both fall in the middle. Average these 2 nos. to get the
median .
𝑋 =
10+15
2
= 12.5
Solutions: You will need to organize the data.
5, 5, 10, 10, 10, 15, 15, 15, 20, 25
Mode: Two numbers appear most often: 10 and 15.
There are three 10’s and three 15’s.
In this example there are two answers for the mode.
𝑋 =10 and 15 (Bimodal)
Range: The difference of highest and lowest score.
Range = 25 – 5 = 20.
Midrange: Sum of highest and lowest values, divided by two.
Midrange =
25 + 5
=
2
15.
Given: 72, 86, 92, 63 and 77.
Mean : 𝑋 =
80 =
80 =
𝑥
𝑛
72+ 86+ 92+ 63 + 77 + n
390+𝒏
6
480 = 390 + n
n = 90
6
• Mean: or average
The sum of a set of data divided by the number of data.
(Do not round your answer unless directed to do so.)
• Median: The middle value, or the mean of the middle two values,
when the data is arranged in numerical order.
• Mode: The value (number) that appears the most often.
It is possible to have more than one mode (bimodal), and it is
possible to have no mode. If there is no mode, write "no mode", do
not write zero (0)
• Range: the difference of the highest and lowest value
• Midrange: sum of highest and lowest values, divided by two.
3
5
1
4
2
3
5
1
4
2
3
5
1
4
2
Let’s do it!
Type discord. com in your
chrome then log in as student.
Thank you for listening
and
God bless you …