#### Solved Examples and Worksheet for Interpreting Scatter Plots

Q1A wholesale dealer of stationery products plots the scatter diagram of his income through the years 1985 to 2000.What is his income in the year 1990?

A. $45,000 B.$40,000
C. $50,000 D.$35,000

Step: 1
The height of each point in the graph indicates the income (in $1000) of the dealer in the particular year. Step: 2 From the graph, the incomes of the dealer in 1985, 1990, 1995 and 2000 are$40000, $45000,$35000, and $50000. Step: 3 The income of the dealer in 1990 was$45000.
Correct Answer is :   $45,000 Q2What is the decrease in the consumption of goods from the year 1999 to 2000 as found in the scatter plot? A. 10 million tons B. 35 million tons C. 25 million tons D. 30 million tons Step: 1 From the plot the consumption of the goods in 1999 was 35 million tons. Step: 2 The consumption of the goods in the year 2000 was 25 million tons. Step: 3 So, the decrease in the consumption of goods is 35 - 25 = 10 million tons. Correct Answer is : 10 million tons Q3The scatter plot shows the number of hours children of different ages sleep. Find how many extra hours a 4 year old child sleeps than a 7 year old child. A. 4 B. 3 C. 7 D. 5 Step: 1 The height of each point in the scatter plot indicates the number of hours a child of the particular age sleeps for. Step: 2 From the graph, the number of hours a 4 year old child sleeps is 14. [The vertical coordinate of the point corresponding to 4 years is 14.] Step: 3 From the graph, the number of hours a 7 year old child sleeps is 10. [The vertical coordinate of the point corresponding to 7 years is 10.] Step: 4 The difference between the number of sleeping hours of a 4 year old and 7 year old child = 14 - 10 = 4 hours. [Subtract 10 from 14.] Step: 5 So, a 4 year old child sleeps for 4 more hours than a 7 year old child. Correct Answer is : 4 Q4The scatter plot shows the number of cars sold in different quarters of the year 1995. Between which two quarters did the number of cars sold decline? A. 1st - 2nd B. 2nd - 3rd C. 3rd - 4th D. The sales never declined Step: 1 The number of cars sold in different quarters of the year 1995 is shown on the given scatter plot. Step: 2 The number of cars sold in the 1st quarter of the year 1995 = 100. Step: 3 The number of cars sold in the 2nd quarter of the year 1995 = 150. Step: 4 The number of cars sold in the 3rd quarter of the year 1995 = 250. Step: 5 The number of cars sold in the 4th quarter of the year 1995 = 200. Step: 6 By looking at the above data, we notice that, the number of cars sold is increased from 1st quarter to 3rd quarter, and decreased from 3rd quarter to 4th quarter. Step: 7 Therefore, in between 3rd and 4th quarters the number of cars sold is declined. Correct Answer is : 3rd - 4th Q5Paula drives at a constant speed from St. Paul to Providence. The scatter plot shows the distance traveled by her at various times. What is the speed at which she is driving? A. 75 mph B. 50 mph C. 100 mph D. 80 mph Step: 1 Each point on the scatter plot represents the distance in miles traveled by Paula by the particular time. Step: 2 Speed = Distancetime [Speed is defined as the rate of distance traveled.] Step: 3 So, the speed at which Paula drives = 1503= 50 mph [Divide the vertical coordinate of any point by the corresponding horizontal coordinate.] Step: 4 So, Paula is driving at 50 mph speed from St. Paul to Providence. Correct Answer is : 50 mph Q6Valerie drives at a constant speed from Milan to Rosedale. The scatter plot shows the distance traveled by her at various times. What is the speed at which she is driving? A. 75 mph B. 50 mph C. 80 mph D. 100 mph Step: 1 Each point on the scatter plot represents the distance in miles traveled by Valerie by the particular time. Step: 2 Speed = Distancetime [Speed is defined as the rate of distance traveled.] Step: 3 So, the speed at which Valerie drives = 1002= 50 mph [Divide the vertical coordinate of any point by the corresponding horizontal coordinate.] Step: 4 So, Valerie is driving at 50 mph speed from Milan to Rosedale. Correct Answer is : 50 mph Q7The scatter plot represents the relationship between the weekly pay and the number of hours worked per week in a month. What was the increase in the weekly pay as the number of hours worked increased from 3 to 9? A.$40
B. $10 C.$30
D. $20 Step: 1 The height of each point in the plot represents the number of hours worked corresponding to the weekly pay. Step: 2 The weekly pay is$10 when the number of hours worked per week is 3.
[The corresponding value of the weekly pay is $10 when the height of the point represents the value 3.] Step: 3 The weekly pay is$30 when the number of hours worked per week is 9.
[The corresponding value of the weekly pay is $30 when the height of the point represents the value 9.] Step: 4 Increase in the weekly pay with the increase in the number of hours worked from 3 to 9 = Weekly pay when the number of hours worked is 9 - Weekly pay when the number of hours worked is 3 =$30 - $10 =$20
[Substitute and subtract.]
Step: 5
So, the increase in the weekly pay as the number of hours worked increases from 3 to 9 is $20. Correct Answer is :$20
Q8The scatter plot represents the times taken by Frank to cover different distances. What was the time taken to cover the total distance?

A. 20 sec
B. 40 sec
C. 30 sec
D. 10 sec

Step: 1
The height of each point in the plot represents the time taken to cover the corresponding distance.
Step: 2
From the plot, the total distance recorded is 400 m.
[The final point represents a distance of 400 m.]
Step: 3
The vertical coordinate corresponding to the distance of 400 m covered is 40.
Step: 4
So, the time taken to cover the total distance is 40 sec.
Correct Answer is :   40 sec
Q9The scatter plot represents the contributions made by a few people to an orphanage in the last 3 years. What is the minimum contribution made to the orphanage?

A. $1,000 B.$3,000
C. $2,000 D.$4000

Step: 1
The height of each point in the plot represents the contribution made in that particular year.
Step: 2
The height of the point corresponding to the 1st year represents the value $1000, which is the least. Step: 3 So, the minimum contribution made to the orphanage was$1,000.
Correct Answer is :   $1,000 Q10The scatter plot displays the weight of Dennis as he grew old. What was his weight when he was 20 years old? A. 100 lb B. 50 lb C. 175 lb D. 125 lb Step: 1 In the scatter plot, the horizontal axis represents Dennis's age and the vertical axis represents his weight in lb. Step: 2 The vertical distance of each point in the scatter plot indicates the weight of Dennis as he grew old. Step: 3 From the graph, the vertical distance of the point corresponding to 20 is 100. Step: 4 So, Dennis weighed 100 lb when he was 20 years old. Correct Answer is : 100 lb Q11The scatter plot displays the weight of Frank as he grew old. At what age was his weight 175 lb? A. 10 years B. 20 years C. 60 years D. 30 years Step: 1 In the scatter plot, the horizontal axis represents Frank's age and the vertical axis represents his weight in lb. Step: 2 The vertical distance of each point in the scatter plot indicates the weight of Frank as he grew older. Step: 3 From the graph, the vertical distance of the point corresponding to age 60 is 175. Step: 4 So, Frank's weight was 175 lb when he was 60 years old. Correct Answer is : 60 years Q12A wholesale dealer of stationery products plots his income through the years 1985 to 2000 in a diagram. In which year did he have the least income ? A. 1985 B. 2000 C. 1990 D. 1995 Step: 1 The height of each point in the graph indicates the income (in$1000) of the dealer in the particular year.
Step: 2
From the graph, the incomes of the dealer in 1985, 1990, 1995 and 2000 are $40000,$45000, $35000 and$50000 respectively.
Step: 3
The income of the dealer in the year 1995 was the least.
Q13The scatter plot displays the income earned by a wholesale dealer of stationery products through the years 1985 to 2000. What was his income in the year 2000?

A. $45,000 B.$40,000
C. $50,000 D.$35,000

Step: 1
In the scatter plot, the horizontal axis indicates the year and the vertical axis indicates the income (in $1000) earned by the wholesale dealer. Step: 2 The height of each point in the graph indicates the income (in$1000) of the dealer in the particular year.
Step: 3
From the graph, the vertical coordinate of the point corresponding to the year 2000 is 50.
Step: 4
So, the income of the wholesale dealer in 2000 was $50,000. Correct Answer is :$50,000
Q14The scatter plot shows the number of hours children of different ages sleep. Find the number of extra hours a 2 year old child sleeps compared to a 6 year old child.

A. 7
B. 5
C. 8
D. 6

Step: 1
The height of each point in the scatter plot indicates the number of hours a child of the particular age sleeps for.
Step: 2
From the graph, the number of hours a 2 year old child sleeps is 18.
[The vertical coordinate of the point corresponding to 2 years is 18.]
Step: 3
From the graph, the number of hours a 6 year old child sleeps is 12.
[The vertical coordinate of the point corresponding to 6 years is 12.]
Step: 4
The difference between the number of sleeping hours of a 2 year old and 6 year old child = 18 - 12 = 6 hours
[Subtract 12 from 18.]
Step: 5
So, a 2 year old child sleeps for 6 more hours than a 6 year old child.
Q15Using the scatter plot and the trend line, estimate the test score of a student who studied for 20 hours.

A. 80
B. 83
C. 85
D. 81

Step: 1
Draw a vertical line starting from 20 hours in the scatter plot. This line intersects the trend line at a point.
Step: 2
From the intersection, draw a horizontal line that intersects the y-axis. This intersection point on the y-axis gives the required test score as the y-axis represents the test scores.
Step: 3
So, a student who studied for 20 hours would have scored about 83 points.