Question

A social scientist is studying the use of Spotify by college students. A sample of 54 students revealed they played the following number of songs on Spotify over the last month.

66 12 80 70 52 25 30 17 187 63 75 12 113 74 139 89 142 135 52 15 96 85 53 47 46 23 45 114 82 14 33 39 68 163 124 103 88 29 24 61 42 60 56 32 92 67 86 18 67 57 107 145 100 166

Organize the above information into a frequency distribution

(a) How many classes would you suggest?

(b) What is the most suitable class interval?

(c) What is the lower limit of the initial class?

(d) Create the frequency distribution

(e) Construct a histogram. The histogram should have a relevant title. What conclusions can you reach based on the information presented in the histogram?

Answer 1

A frequency distribution organizes data into classes of equal width, and a histogram graphically represents this distribution. The number of classes and class interval are determined based on the data range, with a suitable lower limit for the initial class. Conclusions from the histogram may reveal trends in college students' Spotify usage.

Step-by-step explanation:

A frequency distribution is a way to organize data into a chart with classes or groups of equal width. In constructing a frequency distribution for the number of songs played on Spotify by college students, the following steps can be taken:

1. Determine the number of classes suggested, which typically ranges between 5 and 20 to ensure clarity in data representation.
2. Find the range of the data (maximum value - minimum value) and divide it by the number of classes to determine the most suitable class interval.
3. Set the lower limit of the initial class based on the smallest data value.
4. Count how many data points fall into each class and fill out the frequency distribution table.

A histogram is a graphical representation of a frequency distribution with bars. Each bar represents the frequency of data points within the corresponding class. To create a histogram:

1. Use the class limits to establish the horizontal axis.
2. Draw bars that correspond to the frequency of each class without any gaps between bars.
3. Label the histogram with a relevant title and axis labels.

Conclusions from the histogram could involve identifying any trends such as skewness, peaks, or the distribution shape. These can offer insights into the music listening habits of the surveyed students.