Question

5 from unit 1, lesson 2
the data set represents the responses, in degrees fahrenheit, collected to answer the question \how hot is the sidewalk during the school day?\.
92 95 95 95 98 100 100 100 103 105 105 111 112 115
115 116 117 117 118 119 119 119 119 119 119
a. create a dot plot to represent the distribution of the data.
b. create a histogram to represent the distribution of the data.
c. which display gives you a better overall understanding of the data? explain your reasoning.

6 from unit 1, lesson 1
is \what is the area of the floor in this classroom?\ a statistical question? explain your reasoning.

algebra 1

Explanation:

Problem 5a: Create a dot plot

Step 1: Identify unique values and frequencies

First, list the unique temperature values from the data set: 92, 95, 98, 100, 103, 105, 111, 112, 115, 116, 117, 118, 119. Then, count the frequency (number of times each value appears):

• 92: 1
• 95: 3
• 98: 1
• 100: 3
• 103: 1
• 105: 2
• 111: 1
• 112: 1
• 115: 2 (Wait, original data: first row 115, second row 115? Wait original data: first row: 92, 95, 95, 95, 98, 100, 100, 100, 103, 105, 105, 111, 112, 115; second row: 115, 116, 117, 117, 118, 119, 119, 119, 119, 119, 119. So let's recount:
• 92: 1
• 95: 3 (first row: three 95s)
• 98: 1 (first row)
• 100: 3 (first row: three 100s)
• 103: 1 (first row)
• 105: 2 (first row: two 105s)
• 111: 1 (first row)
• 112: 1 (first row)
• 115: 2 (first row: 115, second row: 115)
• 116: 1 (second row)
• 117: 2 (second row: two 117s)
• 118: 1 (second row)
• 119: 6 (second row: six 119s)

Step 2: Draw the dot plot

On the horizontal axis, label the temperature values (92, 95, 98, 100, 103, 105, 111, 112, 115, 116, 117, 118, 119). For each value, place a dot above it corresponding to its frequency. For example, above 92, place 1 dot; above 95, place 3 dots; above 119, place 6 dots, etc.

Problem 5b: Create a histogram

Step 1: Determine bin width (class interval)

Let's choose a bin width. Let's see the data range: minimum is 92, maximum is 119. Let's use bins of width 10: 90 - 100, 100 - 110, 110 - 120. Wait, but let's check the data:

• 90 - 100: values 92, 95, 95, 95, 98, 100, 100, 100. Wait, 100 is included? Wait, usually histograms are left-inclusive or right-inclusive. Let's define bins as [90, 100), [100, 110), [110, 120).

• [90, 100): values 92, 95, 95, 95, 98. Wait, 100 is not included here. Wait, 100 is in [100, 110). Wait, original data: 92, 95 (3), 98, 100 (3), 103, 105 (2), 111, 112, 115 (2), 116, 117 (2), 118, 119 (6).

So:

• [90, 100): 92, 95, 95, 95, 98. That's 1 + 3 + 1 = 5? Wait 92 (1), 95 (3), 98 (1): total 5.

• [100, 110): 100 (3), 103 (1), 105 (2). Total 3 + 1 + 2 = 6.

• [110, 120): 111 (1), 112 (1), 115 (2), 116 (1), 117 (2), 118 (1), 119 (6). Let's calculate: 1 + 1 + 2 + 1 + 2 + 1 + 6 = 14.

Wait, but let's check the total number of data points. First row: 14 values (92, 95, 95, 95, 98, 100, 100, 100, 103, 105, 105, 111, 112, 115). Second row: 11 values (115, 116, 117, 117, 118, 119, 119, 119, 119, 119, 119). Wait 14 + 11 = 25? Wait my earlier count was wrong. Let's recount the data:

First row: 92, 95, 95, 95, 98, 100, 100, 100, 103, 105, 105, 111, 112, 115. That's 14 numbers.

Second row: 115, 116, 117, 117, 118, 119, 119, 119, 119, 119, 119. That's 11 numbers. Total: 14 + 11 = 25.

So let's recount frequencies:

• 92: 1

• 95: 3 (positions 2,3,4)

• 98: 1 (position 5)

• 100: 3 (positions 6,7,8)

• 103: 1 (position 9)

• 105: 2 (positions 10,11)

• 111: 1 (position 12)

• 112: 1 (position 13)

• 115: 2 (position 14, 15)

• 116: 1 (position 16)

• 117: 2 (positions 17,18)

• 118: 1 (position 19)

• 119: 6 (positions 20 - 25: 6 numbers)

Now, total: 1+3+1+3+1+2+1+1+2+1+2+1+6 = 25. Correct.

Now, for histogram bins: let's choose bin width 5. So bins: 90 - 95, 95 - 100, 100 - 105, 105 - 110, 110 - 115, 115 - 120. Wait, but 92 is in 90 - 95, 95 is in 95 - 100? Wait, better to use inclusive on the left, exclusive on the right: [90, 95), [95, 100), [100, 105), [105, 110), [110, 115), [115, 120).

• [90, 95): 92. Frequency: 1.

• [95, 100): 95 (3), 98 (1). Frequency: 3 + 1 = 4.

• [100, 105): 100 (3), 103 (1). Frequency: 3 + 1 = 4.

• [105, 110): 105 (2). Frequency: 2.

• [110, 115): 111 (1), 112 (1). Frequency: 1 + 1 = 2.

• [115, 120): 115 (2), 116 (1), 117 (2), 118 (1), 119 (6). Frequency: 2 + 1 + 2 + 1 + 6 = 12.

Now, draw the histogram: x-axis with bins, y-axis with frequency. For each bin, draw a bar with height equal to its frequency.

Problem 5c: Which display is better?

A dot plot shows the exact frequency of each individual data point, which is good for seeing the distribution of each value. A histogram groups data into bins, which is good for seeing the overall shape (e.g., skewness, clusters). If we want to see the exact counts of each temperature, the dot plot is better. If we want to see the general distribution (e.g., most temperatures are high, around 115 - 120), the histogram is better. But often, the histogram gives a better overall understanding of the data's shape and spread, especially with larger data sets, as it reduces clutter from individual points and shows the distribution's form (e.g., is it skewed, uniform, etc.). However, the dot plot is better for seeing the exact frequency of each value. Depending on the goal, but typically, the histogram (for part b) or dot plot (for part a) – but the question is which display (dot plot or histogram) gives a better overall understanding. The histogram is better for seeing the overall distribution (shape, center, spread) because it groups data into intervals, making it easier to see patterns like clusters or skewness, whereas the dot plot shows individual data points which can be cluttered with many points (like 119 has 6 dots). So the histogram (part b's display) might give a better overall understanding as it summarizes the data into a more interpretable shape.

Problem 6: Is "What is the area of the floor in this classroom?" a statistical question?

Answer:

s:

5a: Dot Plot

• Horizontal axis: Temperatures (92, 95, 98, 100, 103, 105, 111, 112, 115, 116, 117, 118, 119)
• Dots above each temperature: 1 dot for 92, 3 dots for 95, 1 dot for 98, 3 dots for 100, 1 dot for 103, 2 dots for 105, 1 dot for 111, 1 dot for 112, 2 dots for 115, 1 dot for 116, 2 dots for 117, 1 dot for 118, 6 dots for 119.

5b: Histogram

• Bins (e.g., [90,95), [95,100), [100,105), [105,110), [110,115), [115,120))
• Frequencies: 1, 4, 4, 2, 2, 12
• Draw bars with heights 1, 4, 4, 2, 2, 12 for each bin.

5c:

The histogram (or dot plot, depending on reasoning) – typically, the histogram gives a better overall understanding as it shows the data's distribution (shape, clusters) more clearly by grouping into intervals, reducing clutter from individual points, and highlighting patterns like the high frequency of temperatures above 110. The dot plot shows exact counts but can be cluttered with many points (e.g., 119 has 6 dots), while the histogram summarizes the data into a more interpretable shape.

6:

No, it is not a statistical question. A statistical question requires variability (multiple possible answers or a distribution of data), but the area of this specific classroom's floor is a single fixed value, so there is no variability.