Question 1·Easy·One-Variable Data Distributions; Measures of Center and Spread
The dot plot below shows the number of sales calls completed by each of seven sales representatives in one day.
What is the median number of sales calls completed?
For dot plot median questions, first quickly count the total number of dots; if it’s odd, compute the middle position with . Then, starting from the left, count dots up to that position and read the corresponding value from the axis. Avoid mixing up the median with the minimum, maximum, or the value that appears most often, and be careful not to stop one dot too early or too late when locating the middle.
Hints
Think about what the median means
The median is the middle value of a data set when the numbers are arranged from least to greatest. It is not necessarily the smallest, largest, or most common value.
Use the total number of dots
Count how many dots are on the plot. Since each dot is one data value, this tells you how many numbers are in the data set. For an odd number of values, the median is the single middle one.
Find the position of the middle value
If there are values and is odd, the median’s position in the ordered list is . After you know that position, count the dots from left to right until you reach that position, and see which number on the axis that dot is above.
Desmos Guide
Enter the data as a list
From the dot plot, write down all the data values (the number of calls for each representative), repeating a number as many times as there are dots above it. In Desmos, type something like L1 = {a,b,c,d,e,f,g} where each letter is one of the numbers from the plot.
Use Desmos to compute the median
On a new line in Desmos, type median(L1). Desmos will output a single number, which is the median of your data set. Match that number to the correct choice in the problem.
Step-by-step Explanation
Count how many data values there are
Each dot in the dot plot represents one sales representative’s number of calls. Count all the dots on the plot; there are 7 dots total.
For a data set with an odd number of values (like 7), the median is the single middle value when the data are arranged from least to greatest.
Find which position is the median
When there are data values and is odd, the position of the median in the ordered list is given by .
Here, , so the median is the th value in the ordered list.
So you need to figure out what number of calls corresponds to the 4th dot when the dots are read in order from smallest to largest.
Locate the 4th value on the dot plot
Starting from the leftmost dot on the plot, count the dots from left to right: 1st, 2nd, 3rd, and then the 4th dot. The 4th dot lines up above 10 on the horizontal axis.
Therefore, the median number of sales calls is 10, which corresponds to choice B).