Question

4 from unit 1, lesson 3
the data represent the number of ounces of water that 26 students drank the day before a test at school:
8 8 8 16 16 16 32 32 32 32 32 32 64 64 64 64 64 64 80 80 80 80 88 88 88 88
a. create a dot - plot for the data.
b. create a box plot for the data.
c. what information about the data is provided by the dot plot?
d. what information about the data is provided by the box plot?
e. it was recommended that students drink 48 or more ounces of water. how could you use a histogram to easily display the number of students who drank the recommended amount?

Explanation:

Step1: Organize data for dot - plot

List unique values: 8, 16, 32, 64, 80, 88. Count frequencies: 8 appears 3 times, 16 appears 3 times, 32 appears 5 times, 64 appears 5 times, 80 appears 4 times, 88 appears 4 times. Then place dots above corresponding values on a number - line.

Step2: Find quartiles for box - plot

First, order the data. There are \(n = 26\) data points. The median (\(Q_2\)) is the average of the 13th and 14th ordered values. The lower half of the data has 13 values, and its median (\(Q_1\)) is the 7th value. The upper half of the data has 13 values, and its median (\(Q_3\)) is the 20th value. The minimum is 8 and the maximum is 88. Draw a box from \(Q_1\) to \(Q_3\), a line at \(Q_2\) inside the box, and whiskers from the box to the minimum and maximum.

Step3: Analyze dot - plot info

A dot plot shows the exact frequency of each data value. It can show the mode (most frequent value), gaps in the data, and clusters of data points.

Step4: Analyze box - plot info

A box plot shows the five - number summary (minimum, \(Q_1\), median (\(Q_2\)), \(Q_3\), maximum). It gives information about the spread and skewness of the data. The length of the box represents the inter - quartile range (\(IQR=Q_3 - Q_1\)).

Step5: Histogram for recommended amount

For a histogram to show the number of students who drank 48 or more ounces of water, we would create bins. For example, bins could be 48 - 55, 56 - 63, 64 - 71, 72 - 79, 80 - 87. Count the number of data points in each bin that are 48 or more and draw bars with heights corresponding to these counts.

Answer:

a. A dot plot has dots placed above the values 8, 16, 32, 64, 80, 88 with frequencies 3, 3, 5, 5, 4, 4 respectively on a number - line.
b. The box plot has a minimum of 8, \(Q_1\) (7th value in ordered data), median (\(Q_2\)) (average of 13th and 14th values in ordered data), \(Q_3\) (20th value in ordered data), and a maximum of 88.
c. Exact frequencies, mode, gaps, and clusters.
d. Five - number summary, spread, and skewness.
e. Create bins starting from 48 and count the number of data points in each bin to draw bars for the histogram.