Question

slow country tunes here are the lengths, in minutes, of the 50 most popular mp3 downloads of songs by country artist dierks bentley. 4.2 4.0 3.9 3.8 3.7 4.7 3.4 4.0 4.4 5.0 4.6 3.7 4.6 4.4 4.1 3.0 3.2 4.7 3.5 3.7 4.3 3.7 4.8 4.4 4.2 4.7 6.2 4.0 7.0 3.9 3.4 3.4 2.9 3.3 4.0 4.2 3.2 3.4 3.7 3.5 3.4 3.7 3.9 3.7 3.8 3.1 3.7 3.6 4.5 3.7 4. create a dotplot, stemplot, and histogram for the data above. 5. what four categories would we use to analyze the distribution? 6. which graph do you think displays the data most clearly? explain.

Explanation:

Step1: Create dot - plot

For each data value (length of song in minutes), place a dot above the corresponding value on a number line. For example, for the value 4.2, place a dot above 4.2 on the number line. Repeat for all 50 data points.

Step2: Create stemplot

Separate each data value into a stem (the integer part) and a leaf (the decimal part). For example, for 4.2, the stem is 4 and the leaf is 2. List the stems in a vertical column and then place the corresponding leaves to the right of each stem in ascending order.

Step3: Create histogram

1. First, determine the range of the data. The minimum value is 2.9 and the maximum is 7.0.
2. Decide on the number of intervals (bins). Let's say we choose 5 intervals. The width of each interval is $\frac{7.0 - 2.9}{5}=\frac{4.1}{5}=0.82\approx0.8$. So our intervals could be 2.9 - 3.7, 3.7 - 4.5, 4.5 - 5.3, 5.3 - 6.1, 6.1 - 6.9.
3. Count the number of data values that fall into each interval to get the frequency. For example, count how many values are in the 2.9 - 3.7 interval.

Step4: Answer question 5

The four categories to analyze the distribution are: center (e.g., mean, median), spread (e.g., range, standard - deviation), shape (e.g., symmetric, skewed), and outliers (data points that are far from the rest of the data).

Step5: Answer question 6

The stemplot may display the data most clearly as it shows all the individual data values while also giving an idea of the distribution shape. The dot - plot also shows individual values but can get cluttered for a large number of data points. The histogram groups the data into intervals and may lose some of the individual - value information.

Answer:

1. Dot - plot: Created by placing dots for each data value on a number line. Stemplot: Created by separating data into stems and leaves. Histogram: Created by determining intervals, counting frequencies.
2. Center, spread, shape, outliers.
3. The stemplot may display the data most clearly as it shows individual values and distribution shape without getting too cluttered for this data set.