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 98 100 100 103 105 105 111 112
115 115 116 117 117 118 119 119 119 119 119
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.

Explanation:

Step1: Create dot - plot

1. First, list all the unique values in the data set: 92, 95, 98, 100, 103, 105, 111, 112, 115, 116, 117, 118, 119.
2. Then, for each value, count the number of times it appears in the data set. For example, 92 appears 1 time, 95 appears 4 times, etc.
3. On a number - line, place a dot above each value for each occurrence.

Step2: Create histogram

1. Decide on the bin intervals. A reasonable choice could be bins of width 5, e.g., 90 - 94, 95 - 99, 100 - 104, 105 - 109, 110 - 114, 115 - 119.
2. Count the number of data points that fall into each bin. For the bin 90 - 94, there is 1 data point (92). For the bin 95 - 99, there are 5 data points (4 95s and 1 98), etc.
3. Draw a bar for each bin with the height corresponding to the frequency of data points in that bin.

Step3: Compare the displays

1. The dot - plot shows the exact number of occurrences of each individual value. It is good for seeing the exact distribution of individual data points and any outliers.
2. The histogram groups the data into intervals and gives a better sense of the overall shape of the distribution (e.g., symmetric, skewed). It is useful for identifying trends in the data at a glance.
3. The answer depends on the focus. If we want to know exact frequencies of each value, the dot - plot is better. If we want to understand the overall shape and trends in the data, the histogram is better.

Answer:

a. A dot - plot is created by placing a dot for each occurrence of each unique value on a number - line.
b. A histogram is created by counting the number of data points in chosen bin intervals and drawing bars with heights corresponding to those frequencies.
c. If the focus is on exact frequencies of individual values, the dot - plot is better. If the focus is on the overall shape and trends in the data, the histogram is better.