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. dot plot with x - axis: 0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.30, 0.31, 0.32, 0.33, 0.34; y - axis with dots 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. dot plot with x - axis: 112, 114, 116, 118, 120, 122, 124; y - axis with dots 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?

Explanation:

Problem 4 (Dot Plot of Rock Weights)

• Bell - shaped: A bell - shaped distribution has a single peak and tapers off symmetrically on both sides. This dot plot has two peaks, so it's not bell - shaped.
• Bimodal: A bimodal distribution has two distinct peaks. Looking at the dot plot, we can see two areas (around 0.27 and 0.31) with a relatively high number of dots (peaks), so it is bimodal.
• Skewed: A skewed distribution has most of the data on one side and a tail on the other. This plot doesn't show a long tail on one side, so it's not skewed.
• Symmetric: A symmetric distribution has data evenly distributed around a central point, with the left and right sides mirroring each other. This plot has two peaks, not a single central peak with symmetry, but the overall shape (with two peaks) can be considered symmetric in the sense that the data is balanced around the middle range (between the two peaks) and there is no strong skew. Also, the presence of two peaks (bimodal) and the lack of skew can make it symmetric in a broader sense.
• Uniform: A uniform distribution has data evenly spread out with no peaks. This plot has peaks, so it's not uniform.

Step 1: Count the number of dots for each wage

• For 112: 1 dot
• For 113: 1 dot (assuming the second dot is at 113, since it's between 112 and 114)
• For 116: 3 dots
• For 118: 2 dots
• For 119: 2 dots (assuming the dots at 119, between 118 and 120)
• For 124: 3 dots

Wait, actually, let's list the data points properly from the dot plot:

• 112: 1
• 113: 1 (the dot between 112 and 114)
• 116: 3
• 118: 2
• 119: 2 (the dot between 118 and 120)
• 124: 3

Now, calculate the sum of (wage * number of students with that wage):

• \(112\times1 + 113\times1+116\times3 + 118\times2+119\times2 + 124\times3\)

Step 2: Calculate each term

• \(112\times1=112\)
• \(113\times1 = 113\)
• \(116\times3=348\)
• \(118\times2 = 236\)
• \(119\times2=238\)
• \(124\times3 = 372\)

Step 3: Sum all the terms

Sum \(=112 + 113+348+236+238+372\)
\(112+113 = 225\); \(225+348 = 573\); \(573+236 = 809\); \(809+238 = 1047\); \(1047+372=1419\)

Step 4: Calculate the mean

Mean \(=\frac{\text{Total sum}}{\text{Number of students}}=\frac{1419}{12}=118.25\)

Interpretation: The mean weekly wage of the 12 college students is $118.25. This means that if we were to distribute the total wages earned evenly among all 12 students, each student would earn approximately $118.25 per week.

Step 1: Order the data

First, list the data points in ascending order. The data points are: 112, 113, 116, 116, 116, 118, 118, 119, 119, 124, 124, 124 (since we have 1 (112), 1 (113), 3 (116s), 2 (118s), 2 (119s), 3 (124s))

Step 2: Find the middle position

Since there are \(n = 12\) data points (even number), the median is the average of the \(\frac{n}{2}=6^{\text{th}}\) and \((\frac{n}{2}+ 1)=7^{\text{th}}\) values.

Step 3: Identify the 6th and 7th values

• The 1st value: 112
• 2nd: 113
• 3rd: 116
• 4th: 116
• 5th: 116
• 6th: 118
• 7th: 118

Step 4: Calculate the median

Median \(=\frac{118 + 118}{2}=118\)

Interpretation: The median weekly wage is $118. This means that half of the 12 college students earned less than or equal to $118 per week, and half earned more than or equal to $118 per week.

Answer:

B. bimodal, D. symmetric

Problem 5a (Mean of Weekly Wages)