Question

college math: --- exit ticket week 11

1. list the three main measures of central tendency.
2. find the mean, median, and mode for the following set of data:

6, 8, 6, 10, 6, 12

• mean =
• median =
• mode =

1. which measure best represents this data set? why?

self-reflection

1. rate your understanding of todays topic (circle one):

not clear somewhat clear very clear

Explanation:

Step1: Calculate the mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here, $x_{1}=6,x_{2}=8,x_{3}=6,x_{4}=10,x_{5}=6,x_{6}=12$, and $n = 6$.
$\sum_{i=1}^{6}x_{i}=6 + 8+6 + 10+6 + 12=48$
$\bar{x}=\frac{48}{6}=8$

Step2: Calculate the median

First, order the data set: $6,6,6,8,10,12$.
Since $n = 6$ (even), the median $M=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}$.
$x_{\frac{6}{2}}=x_{3}=6$, $x_{\frac{6}{2}+1}=x_{4}=8$
$M=\frac{6 + 8}{2}=7$

Step3: Calculate the mode

The mode is the most - frequently occurring value. In the data set $6,6,6,8,10,12$, the value $6$ occurs 3 times.

Answer:

Mean = $8$
Median = $7$
Mode = $6$