a group of students created a dot plot of their heights. based on the dot plot, find the mean and median…

Explanation:

Step1: Count the number of data - points

Count the number of dots in the dot - plot. There are 1 + 2+3 + 4+3 + 2+1=16 data - points.

Step2: Calculate the sum of all data - points

[ \begin{align*} &4.0\times1+4.25\times2 + 4.5\times3+4.75\times4+5.0\times3+5.25\times2+5.5\times1\ =&4.0 + 8.5+13.5 + 19.0+15.0+10.5+5.5\ =&76 \end{align*} ]

Step3: Calculate the mean

The mean $\bar{x}=\frac{\text{Sum of data - points}}{\text{Number of data - points}}=\frac{76}{16}=4.75$ feet.

Step4: Find the median

Since there are $n = 16$ data - points (an even number of data - points), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data - points. First, order the data. The ordered data set has 16 values. The 8th and 9th values in the ordered set. Counting the dots from the left, the 8th and 9th values are both 4.75. So the median $M = 4.75$ feet.

Answer:

The mean height of the students is 4.8 feet, and the median height of the students is 4.8 feet. (Note: when rounded to the nearest tenth, both 4.75 rounds to 4.8)