FIND MEAN MEDIAN MODE AND RANGE FROM DOT PLOT

Problem 1 :

Use the line plot. Find the

(i) Mean   (ii) Median   (iii) Mode and (iv) Range 

of the data.

Solution :

Mean :

Writing the given data, we get

0, 0, 0, 1, 1, 1, 1, 2, 2, 4, 6, 6

Number of families who has 0 pets = 3

Number of families who has 1 pet = 4

Number of families who has 4 pets = 1

Number of families who has 6 pets = 2

Mean number of pets

= [3(0) + 1(4) + 4(1) + 6(2)] / (3 + 4 + 1 + 2)

= (0 + 4 + 4 + 12) / 10

= 20 / 10

= 2

So, mean number of pets is 2.

Median :

Total number of entries = 12

0, 0, 0, 1, 1, 1, 1, 2, 2, 4, 6, 6

median = (6^th + 7^th)/2

= (1 + 1)/2

Median = 1

Mode :

Mode = 1

Range :

Range = largest value - smallest value

= 6 - 0

= 6

Problem 2 :

The dot plot shows the types of pets treated at a vet on one day.

a) How many pets were treated on this day?

b) Find the mode of the data.

c) What percentage of the pets treated were fish?

Solution :

Number of cats = 4

Number of dogs = 6

Number of birds = 3

Number of fishes = 4

other = 3

a) Total number of pets treated on that day :

= 4 + 6 + 3 + 4 + 3

= 20

So, total number of pets treated is 20.

b) Mode :

Mode of the data is dog.

c) Percentage of fishes treated :

Number of fishes = 4

Percentage = (4/20) x 100%

= (1/5) x 100%

= 20%

Problem 3 :

At recess time the sales of drinks were recorded over a three minute period.

O = 100 plus, S = soy milk, C = cola, I = iced tea.

The data was: OSSCI OCISO IOCSO OOOSC SOCOS SOOCO OIOIS

a Draw a dot plot of the data. b What is the mode?

Solution :

a)  

b) 100 plus is the mode.

Problem 3 :

Four girls on a high school track and field team practice the shot put. Each girl made 10 attempts, and the distances measure after each attempt are shown on the plots below.

a)  Which girl’s range of distance was the greatest?

Solution :

Range of distance of Candance's attempts = 41 - 33

= 8

Range of distance of Sara's attempts = 42 -  35

= 7

So, Candance's attempts has greatest attempts of distance.

Problem 4 :

Find the mean, median, and mode of each dot plot.

Solution :

a) 0, 4, 4, 8, 8, 8, 12, 12, 16

Mean :

Mean = [0(1) + 4(2) + 8(3) + 12(2) + 16(1)] / 9

= (0 + 8 + 24 + 24 + 16)/9

= 72/9

= 8

Median :

Total number of entries = 9

Median = (9 + 1)/2 ^th value

= 5^th value

= 8

Mode :

8 is repeated 3 times. so, mode is 3.

b) 10, 10, 15, 15, 15, 20, 20, 20, 20, 25, 25, 25, 25, 30, 30, 35, 40, 40, 45, 45, 45, 50

Mean : 

= [2(10) + 3(15) + 4(20) + 4(25) + 2(30) + 1(35) + 2(40) + 3(45) + 1(50)] / 22

= (20 + 45 + 80 + 60 + 35 + 80 + 135 + 50) / 22

= 505/22

= 22.95

Median :

Total number of entries = 22

Median = (11^th element  + 12th element) / 2

= (25 + 25)/2

= 25

So, median is 25.

Mode :

20 and 25 are modes.