Question

lesson 11 comparing and contrasting data distributions lets investigate variability using data displays and summary statistics. warm - up math talk: mean evaluate the mean of each data set mentally. 1 27 30 33 30 2 61 71 81 91 10 62.5 3 0 100 100 100 100 80 4 0 5 7 12 6 card sort: describing data distributions 1 your teacher will give you a set of cards. take turns with your partner to match a data display with a written statement. a for each match that you find, explain to your partner how you know its a match. b for each match that your partner finds, listen carefully to their explanation. if you disagree, discuss your thinking and work to reach an agreement. 2 after matching, determine if the mean or median is more appropriate for describing the center of the data set based on the distribution shape. discuss your reasoning with your partner. if it is not given, calculate (if possible) or estimate the appropriate measure of center. be prepared to explain your reasoning. i have completed this task.

Explanation:

Step1: Recall mean formula

The mean of a data - set $x_1,x_2,\cdots,x_n$ is $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$.

Step2: Calculate mean for data - set 1

For the data - set $27,30,33$, $n = 3$ and $\sum_{i=1}^{3}x_i=27 + 30+33=90$. So, $\bar{x}=\frac{90}{3}=30$.

Step3: Calculate mean for data - set 2

For the data - set $61,71,81,91,10$, $n = 5$ and $\sum_{i = 1}^{5}x_i=61+71 + 81+91+10=314$. So, $\bar{x}=\frac{314}{5}=62.8$.

Step4: Calculate mean for data - set 3

For the data - set $0,100,100,100,100$, $n = 5$ and $\sum_{i=1}^{5}x_i=0 + 100+100+100+100 = 400$. So, $\bar{x}=\frac{400}{5}=80$.

Step5: Calculate mean for data - set 4

For the data - set $0,5,7,12$, $n = 4$ and $\sum_{i=1}^{4}x_i=0 + 5+7+12=24$. So, $\bar{x}=\frac{24}{4}=6$.

Answer:

1. Mean of data - set 1: 30
2. Mean of data - set 2: 62.8
3. Mean of data - set 3: 80
4. Mean of data - set 4: 6