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 4 :

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 5 :

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.

Problem 6 :

A teacher drew a line segment that was 20 inches long on the blackboard. She asked each of her students to estimate the length of the segment and used their estimates to draw this dot plot.

a. How many students were in the class?

b. Were students generally accurate in their estimates of the length of the line? Explain your reasoning.

Solution :

a) Number of students in the class = 1 + 3 + 1 + 5 + 5 + 3

= 18

So, total number of students is 18.

b) Mean = [16(1) + 17(3) + 18(1) + 19(5) + 20(5) + 21(3)]/18

= (16 + 51 + 18 + 95 + 100 + 63)/18

= 343/18

= 19.0

So, estimated length of line is 19 inches.

Problem 7 :

Determine if each statement is true or false.

a) The range of the data for the heights of softball players is less than the range of the data for the heights of basketball players.

b) The median of the data for the heights of softball players is greater than the median of the data for the heights of basketball players

Solution :

a) Rage of softball players = 66 - 59

= 7

Range of basketball players = 72 - 62

= 10

b) Median of soft balls :

N = 1 + 2 + 1 + 2 + 1 + 5 + 2 + 1

= 15

Median = (N + 1)/2 th term

= 16/2

= 8th term

Median is 64.

Median of basket ball players :

N = 1 + 2 + 1 + 5 + 2 + 1 + 1 + 2

= 15

Median = (N + 1)/2 th term

= 16/2

= 8th term

Median is 68

a) True

b) False