Median-of-ungrouped-data.pptx

Mean - is equal to the sum of the quantities divided by the number of quantities under consideration.

In formula: 𝑥ഥ =

σ𝑋 𝑁

What is the mean of the following data : 12, 24, 36, 48, 60 ?

𝑥ഥ = 𝑥ഥ =

σ𝑋

𝑁 σ 180

5

𝑥ҧ = 36

PICTOWORD

DIAN

MEDIAN

UN

UNGROUP

TA

DATA

MEDIAN OF UNGROUPED DATA BY: MARIVIC DEL ROSARIO CACAL

Sonya‘s Kitchen received an invitation to a food exposition for one person. The service crew of 7 members is very eager to go. To be fair to all, Sonya decided to choose a person whose age is also the median age of her seven members. Sonya’s Kitchen Crew

Service Crew Age

Waiter Cook B Waiter B Cashier Cook A Waitress Manager

18 20 18 19 21 18 47

a) Arrange the ages in numerical order.  18 , 18, 18, 19, 20, 21, 47 - ASCENDING  47, 21, 20, 19, 18, 18, 18 – DESCENDING b) What is the middle value?  18 , 18, 18, 19, 20, 21, 47 - ASCENDING  47, 21, 20, 19, 18, 18, 18 - DESCENDING

c) Is there a crew with this representative age?  Yes. d) How many are younger than this age? Older than this age?  3 crews are younger than 19 and 3 crews are older than 19. e) Who is the representative of Sonya’s Kitchen in the Food Fair?  The cashier.

At the end of the month, Sonya’s kitchen hired another crew member whose age is 22. The data now consist of eight ages: 18, 20, 18, 19, 21, 18, 47, and 22, an even number. How many middle entries are there? Sonya’s Kitchen Crew

a) Arrange the crew’s ages in numerical order.  18 , 18, 18, 19, 20, 21, 22, 47 – ASCENDING  47, 22, 21, 20, 19, 18, 18, 18 – DESCENDING

b) Find the two middle values (ages).  19 and 20 c) Get the average of the two middle values.  19.5

d) What is now the median age?  19.5 e) How many are below this age? Above this age?  4 crews are younger than the median age and 4 crews are older than the median age.

Median – is the middle value or term in a set of data arranged in either ascending or descending order.

It separates an ordered set of data into two equal parts.

• If 𝑛 is odd, the median is the

𝑛+1 𝑡ℎ ( ) 2

quantity.

• If 𝑛 is even, the median is the mean of 𝑛 𝑛 𝑡ℎ 𝑡ℎ ( + 1) and ( ) . 2

2

Group1. Find the median of the following data. Andrea’s scores in 10 quizzes during the first quarter are 8, 7, 6, 10, 9, 5, 9, 6, 10, and 7. Group 2. The library logbook shows that 58, 60, 54, 35 and 97 books, respectively, were borrowed from Monday to Friday last week. Group 3. The front row in a movie theatre has 23 seats. If you were asked to sit in the seat that occupied the median position, in which seat would you have to sit?

Group1. Find the median of the following data. Andrea’s scores in 10 quizzes during the first quarter are 8, 7, 6, 10, 9, 5, 9, 6, 10, and 7.  5, 6, 6, 7, 7, 8, 9, 9, 10, 10 𝑛 10 𝑡ℎ  ( + 1) = ( + 1)𝑡ℎ 2 2 𝑛 𝑡ℎ 10 𝑡ℎ  ( ) = ( ) = 5𝑡ℎ 2 2 7+8  Median = 7.5 2

= 6𝑡ℎ

Group 2. The library logbook shows that 58, 60, 54, 35 and 97 books, respectively, were borrowed from Monday to Friday last week.  35, 54, 58, 60, 97  Median  58

𝑛+1 𝑡ℎ ( ) 2

=

5+1 𝑡ℎ ( ) 2

= 3𝑡ℎ

Group 3. The front row in a movie theatre has 23 seats. If you were asked to sit in the seat that occupied the median position, in which seat would you have to sit?  Median

𝑛+1 𝑡ℎ ( ) 2

24 𝑡ℎ  ( ) 2  12𝑡ℎ seat

=

23+1 𝑡ℎ ( ) 2

Find the median of the following data. 1. 83, 84, 85, 86, 82 2. 80, 82, 84, 86 3. 79, 81, 80, 80, 81 4. 85, 75, 82, 78 5. 75, 83, 82, 80, 76

1. 83, 84, 85, 86, 82  82, 83, 84, 85, 86 2. 80, 82, 84, 86  80, 82, 84, 86 = (82+84)/2 = 83 3. 79, 81, 80, 80, 81  79, 80, 80, 81, 81

4. 85, 75, 82, 78 75, 78, 82, 85 = (78+82)/2 = 80

5. 75, 83, 82, 80, 76 75, 76, 80, 82, 83

ASSIGNMENT Compute for the median score of 20 students in a math quiz. 25, 33, 35, 45, 34, 26, 29, 35, 38, 40, 45, 38, 28, 29, 25, 39, 32, 37, 47, 45.