Question

a teacher gave his spanish students a set of 50 words to memorize. on friday, all 25 of his students took a vocabulary test; the number of words they knew are shown below.
42 47 41 46 43 45 34 43 40 45
44 50 35 37 39 48 38 48 41 37
44 43 43 48 36

1. graph a dot plot of the data given. be sure to include a proper scale and label.
2. graph a histogram for the data given, starting with 34 and using bins that have a width of 3 (so the first starts with 34, the next bin starts with 37, etc.)
3. write a few sentences describing the distribution of friday’s scores above.

Explanation:

Question 7: Dot Plot Construction

Step 1: Identify Data Range

First, find the minimum and maximum values in the data. The data points are: 34, 35, 36, 37, 37, 38, 39, 40, 41, 41, 42, 43, 43, 43, 43, 44, 44, 45, 45, 46, 47, 48, 48, 48, 50. The minimum is 34 and the maximum is 50.

Step 2: Set Up the Scale

Draw a horizontal axis (number line) labeled "Number of Words Known" with a scale from 34 to 50. Mark each integer value from 34 to 50 on the axis.

Step 3: Plot the Dots

For each data point, place a dot above the corresponding value on the number line. Count the frequency of each value:

• 34: 1 dot
• 35: 1 dot
• 36: 1 dot
• 37: 2 dots
• 38: 1 dot
• 39: 1 dot
• 40: 1 dot
• 41: 2 dots
• 42: 1 dot
• 43: 4 dots
• 44: 2 dots
• 45: 2 dots
• 46: 1 dot
• 47: 1 dot
• 48: 3 dots
• 50: 1 dot

Step 1: Define the Bins

The bins start at 34 with a width of 3. So the bins are:

• Bin 1: 34 – 36 (inclusive, since width 3: 34, 35, 36)
• Bin 2: 37 – 39 (37, 38, 39)
• Bin 3: 40 – 42 (40, 41, 42)
• Bin 4: 43 – 45 (43, 44, 45)
• Bin 5: 46 – 48 (46, 47, 48)
• Bin 6: 49 – 51 (49, 50, 51; only 50 is in data)

Step 2: Calculate Frequencies for Each Bin

• Bin 1 (34–36): Values 34, 35, 36. Frequency = 3.
• Bin 2 (37–39): Values 37, 37, 38, 39. Frequency = 4.
• Bin 3 (40–42): Values 40, 41, 41, 42. Frequency = 4.
• Bin 4 (43–45): Values 43, 43, 43, 43, 44, 44, 45, 45. Frequency = 8.
• Bin 5 (46–48): Values 46, 47, 48, 48, 48. Frequency = 5.
• Bin 6 (49–51): Value 50. Frequency = 1.

Step 3: Draw the Histogram

• Vertical axis: "Frequency (Number of Students)".
• Horizontal axis: "Number of Words Known" with bins labeled 34–36, 37–39, 40–42, 43–45, 46–48, 49–51.
• Draw bars for each bin with height equal to their frequency.

First, identify the center (e.g., median), spread (range, interquartile range), and shape (symmetry, skewness, peaks).

• Shape: The distribution has a peak around 43–45 (highest frequency). It is somewhat skewed left (lower values have fewer data points, higher values after the peak decrease gradually).
• Center: The median (middle value of 25 data points) is the 13th value. Ordering data: 34,35,36,37,37,38,39,40,41,41,42,43,43,43,43,44,44,45,45,46,47,48,48,48,50. The 13th value is 43, so median is 43.
• Spread: Range is \( 50 - 34 = 16 \). Most data is between 34 and 50, with a concentration between 40–48.

Answer:

A dot plot with a horizontal axis labeled "Number of Words Known" from 34 to 50. Dots are placed above each value as per their frequencies (e.g., 4 dots above 43, 3 dots above 48, etc.).

Question 8: Histogram Construction