Question

compare and contrast graphs
name
the following data shows the numbers of minutes spent in reading: 12, 15, 18, 20, 22, 22, 25, 25, 25, 28, 30, 31, 32, 35, 35, 42, 44, 46, 48, 55

1. use the intervals 10 - 19, 20 - 29, 30 - 39, 40 - 49 and 50 - 59 to make a histogram of the data.
2. make a circle graph to show the percent of spent in reading with 10 - 19, 20 - 29, 30 - 39, 40 - 49, 50 - 59 minutes.
3. make a line plot of the data

Explanation:

Part 1: Histogram (Tally and Frequency Table)

Step1: Identify data in each interval

• 10 - 19: 12, 15, 18 → 3 values
• 20 - 29: 20, 22, 22, 25, 25, 25, 28 → 7 values
• 30 - 39: 30, 31, 32, 35, 35 → 5 values
• 40 - 49: 42, 44, 46, 48 → 4 values
• 50 - 59: 55 → 1 value

Step2: Create tally marks

• 10 - 19: ||| (3)
• 20 - 29: |||| || (7)
• 30 - 39: |||| | (5)
• 40 - 49: |||| (4)
• 50 - 59: | (1)

Step3: Record frequencies

Interval	Tally	Frequency
20 - 29								7
30 - 39							5
40 - 49						4
50 - 59			1

To make the histogram, draw bars for each interval with heights equal to their frequencies. The x - axis is the intervals (10 - 19, 20 - 29, etc.) and the y - axis is frequency.

Part 2: Circle Graph (Pie Chart)

Step1: Find total frequency

Total data points: \(3 + 7+5 + 4+1=20\)

Step2: Calculate \(\frac{\text{Target Frequency}}{\text{Total Frequency}}\), decimal, and percent for each interval

• 10 - 19: \(\frac{3}{20}=0.15 = 15\%\)
• 20 - 29: \(\frac{7}{20}=0.35 = 35\%\)
• 30 - 39: \(\frac{5}{20}=0.25 = 25\%\)
• 40 - 49: \(\frac{4}{20}=0.20 = 20\%\)
• 50 - 59: \(\frac{1}{20}=0.05 = 5\%\)

Interval	\(\frac{\text{Target Frequency}}{\text{Total Frequency}}\)	Decimal	Percent
20 - 29	\(\frac{7}{20}\)	0.35	35%
30 - 39	\(\frac{5}{20}\)	0.25	25%
40 - 49	\(\frac{4}{20}\)	0.20	20%
50 - 59	\(\frac{1}{20}\)	0.05	5%

To make the circle graph, calculate the central angle for each interval (\(360^{\circ}\times\text{decimal}\)):

• 10 - 19: \(360\times0.15 = 54^{\circ}\)
• 20 - 29: \(360\times0.35 = 126^{\circ}\)
• 30 - 39: \(360\times0.25 = 90^{\circ}\)
• 40 - 49: \(360\times0.20 = 72^{\circ}\)
• 50 - 59: \(360\times0.05 = 18^{\circ}\)

Then draw a circle and divide it into sectors with these central angles, labeling each with the interval and percent.

Part 3: Line Plot

• A line plot (dot plot) has a number line that includes all the data values (12, 15, 18, 20, 22, 25, 28, 30, 31, 32, 35, 42, 44, 46, 48, 55).
• For each data value, place a dot (or X) above the corresponding number on the number line. If a value repeats, stack the dots.
• For example:
• Above 12: 1 dot
• Above 15: 1 dot
• Above 18: 1 dot
• Above 20: 1 dot
• Above 22: 2 dots
• Above 25: 3 dots
• Above 28: 1 dot
• Above 30: 1 dot
• Above 31: 1 dot
• Above 32: 1 dot
• Above 35: 2 dots
• Above 42: 1 dot
• Above 44: 1 dot
• Above 46: 1 dot
• Above 48: 1 dot
• Above 55: 1 dot

Final Answers (Summarized for each part)

1. Histogram: Tally and frequency table as above, histogram with bars of heights 3, 7, 5, 4, 1 for intervals 10 - 19, 20 - 29, 30 - 39, 40 - 49, 50 - 59 respectively.
2. Circle Graph: Table with percentages 15%, 35%, 25%, 20%, 5% for intervals 10 - 19, 20 - 29, 30 - 39, 40 - 49, 50 - 59 respectively, and sectors with central angles \(54^{\circ}\), \(126^{\circ}\), \(90^{\circ}\), \(72^{\circ}\), \(18^{\circ}\).
3. Line Plot: Dot plot with dots stacked above each data value as described.

Answer:

• A line plot (dot plot) has a number line that includes all the data values (12, 15, 18, 20, 22, 25, 28, 30, 31, 32, 35, 42, 44, 46, 48, 55).
• For each data value, place a dot (or X) above the corresponding number on the number line. If a value repeats, stack the dots.
• For example:
• Above 12: 1 dot
• Above 15: 1 dot
• Above 18: 1 dot
• Above 20: 1 dot
• Above 22: 2 dots
• Above 25: 3 dots
• Above 28: 1 dot
• Above 30: 1 dot
• Above 31: 1 dot
• Above 32: 1 dot
• Above 35: 2 dots
• Above 42: 1 dot
• Above 44: 1 dot
• Above 46: 1 dot
• Above 48: 1 dot
• Above 55: 1 dot

Final Answers (Summarized for each part)

1. Histogram: Tally and frequency table as above, histogram with bars of heights 3, 7, 5, 4, 1 for intervals 10 - 19, 20 - 29, 30 - 39, 40 - 49, 50 - 59 respectively.
2. Circle Graph: Table with percentages 15%, 35%, 25%, 20%, 5% for intervals 10 - 19, 20 - 29, 30 - 39, 40 - 49, 50 - 59 respectively, and sectors with central angles \(54^{\circ}\), \(126^{\circ}\), \(90^{\circ}\), \(72^{\circ}\), \(18^{\circ}\).
3. Line Plot: Dot plot with dots stacked above each data value as described.