Create and Interpret Parallel Dot Plots

Dot plots are a quick way to visually represent data. Just like dot plots, if you are considering a large data set it would be best to use another type of graph, but for fairly small size data sets parallel dot plots can help you to quickly see the spread of data and identify any outliers.

Parallel dot plots help you to compare two or more sets of data, which must be plotted against the same scale. This makes the comparison between the data sets easy and ensures it isn't misleading. For example, you cannot have one dot plot for the height of a group of people, and have a parallel dot plot for their weights as these would be in different units. They must be in the same unit and the same scale. When creating a parallel dot plot, it's also really important to make sure you take the time to make sure everything is lined up correctly! 

Examples

question 1

A class was asked to complete $10$10 questions in Mathspace for homework.

a) Which group had the highest median? 

Think: The median is the middle data point after the data has been ordered. As this data is already ordered you need to find the middle data point for both groups and compare them.

Do: Boys - there are $14$14 boys, so the median will be the average of the $7$7th and $8$8th data point. $\frac{8+10}{2}=9$8+102​=9 minutes.

Girls - there are $15$15 girls, so the median data point will be the $8$8th data point. Count along to find the $8$8th point. The median is $7$7 minutes.

So the boys had the higher median.

b) Which group had the largest range? 

Think: You need to calculate the range for each dot plot and then compare. 

Do: for boys the range is $12-2=10$12−2=10. For girls the range is $12-2=10$12−2=10. The range is the same for both groups. 

c) Who had the smallest mode? boys/girls

Think: The mode refers to most often. There can be more than one mode.

Do: Look to see where the graph is tallest. 

Boys - $3$3 boys took $11$11 minutes. 

Girls - $3$3 girls took $10$10 minutes. 

The girls therefore had the smallest mode.

question 2

$20$20 people joined a weight loss class. When they first joined they had their weights measured each week. Their overall weight was plotted each week on a parallel dot plot.

a) After $1$1 week, how has the median weight loss from when the class started?

Think: Make sure you are looking at the correct data set. The median is the middle data point of an ordered set of data.

Do: We know that there are $20$20 people in the class. Therefore the median is in the middle of the $10$10th and $11$11th data points. 

$\frac{3+3}{2}=3$3+32​=3 kilograms

b) After $2$2 weeks, what is the mean weight loss of the class since the class started?

Think: The mean is calculated by adding all the data points together and dividing by the number of data points. We already know there are $20$20 data points. 

Do: $\frac{2+2+3+4+4+4+4+5+5+6+6+7+7+7+8+8+9+9+9+10}{20}$2+2+3+4+4+4+4+5+5+6+6+7+7+7+8+8+9+9+9+1020​ 

= $5.95$5.95 kilograms

Question 3

Question 4