Question

4 from unit 1, lesson 4 the dot plot shows the weight, in grams, of several different rocks. select all the terms that describe the shape of the distribution. a bell - shaped b bimodal c skewed d symmetric e uniform 5 from unit 1, lesson 3 the dot plot represents the distribution of wages earned during a one - week period by 12 college students. a. what is the mean? interpret this value based on the situation. b. what is the median? interpret this value based on the situation. c. would a box plot of the same data have allowed you to find both the mean and the median? 6 from unit 1, lesson 2 the box plot displays the temperature of saunas in degrees fahrenheit. what is the median? learning target + i can calculate mean absolute deviation, interquartile range, mean, and median for a set of data.

Explanation:

Step1: Analyze question 4

By observing the dot - plot of rock weights, we see that the distribution is not bell - shaped, not symmetric, not uniform. There are two peaks, so it is bimodal and not symmetric (skewed).

Step2: Analyze question 5a

Count the number of data points and their values from the dot - plot of weekly wages. There are 12 data points: 112 (1 time), 114 (1 time), 116 (3 times), 118 (2 times), 120 (2 times), 124 (3 times). The sum of the data is \(112\times1 + 114\times1+116\times3 + 118\times2+120\times2+124\times3=112 + 114+348+236+240+372 = 1422\). The mean \(\bar{x}=\frac{1422}{12}=118.5\). Interpretation: On average, the 12 college students earned $118.5 per week.

Step3: Analyze question 5b

Arrange the 12 data points in ascending order: 112, 114, 116, 116, 116, 118, 118, 120, 120, 124, 124, 124. Since \(n = 12\) (even), the median is the average of the \(\frac{n}{2}=6\)th and \((\frac{n}{2}+1)=7\)th ordered data points. Median \(=\frac{118 + 118}{2}=118\). Interpretation: Half of the 12 college students earned less than $118 per week and half earned more.

Step4: Analyze question 5c

A box - plot shows the median (the line inside the box), but not the mean. So the answer is no.

Step5: Analyze question 6

In a box - plot, the median is the line inside the box. For the box - plot of sauna temperatures, the median is 116 degrees Fahrenheit.

Answer:

1. B. bimodal, C. skewed

5.
a. 118.5; On average, the 12 college students earned $118.5 per week.
b. 118; Half of the 12 college students earned less than $118 per week and half earned more.
c. No

1. 116 degrees Fahrenheit