Q 37. - The Practice of Statistics for AP

Question

Feeling sleepy? Students in a college statistics class responded to a survey designed by their teacher. One of the survey questions was “How much sleep did you get last night?” Here are the data (in hours): 

(a) Make a dot plot to display the data.

(b) Describe the overall pattern of the distribution

and any deviations from that pattern.

Step-by-Step Solution

Answer

Part (b) 

• The data is nearly symmetrical in shape.
• Because the highest dots in the dot-plot are at $6$, the time spent in the center is approximately $6$ hours.
• The time span is between $3$ and $11$ hours.
• There do not appear to be any anomalies in the pattern.

Part (a) The dot plot is

Part (a) Step 1: Given information

The table is 

9	6	8	6	8	8	6	6.5	6	7	9	4	3	4
5	6	11	6	3	6	6	10	7	8	4.5	9	7	7

Part (a) Step 2: Concept

To visualize the distribution of a quantitative variable, you can use a dot plot, stem plot, or histogram. A dot plot is a type of graph that shows individual values on a number line. Each observation is divided into a stem and a one-digit leaf in stem plots. The counts (frequencies) or percent's (relative frequencies) of values in equal-width classes are plotted in histograms.

Part (a) Step 3: Explanation

We have information on the students' sleeping hours. A dot plot is a simple graph in which each data value is represented by a dot above its location on a number line. The following is the dot plot of the given data: 

Thus, a dot plot is drawn.

Part (b) Step 1: Explanation

The shape, center, spread, and outliers of distribution can all be used to define its general pattern.

Shape: The Dot plot has a peak at $6$, indicating that the majority of students slept for at least $6$ hours the night before the survey. As a result, the model is $6$ The majority of the pupils slept for$6$ to $9$ hours. The distribution, on the other hand, has a long slope to the right.

Center: The center can be described by selecting a value that splits the data in half. As a result, roughly half of the people choose greater values while the other half choose smaller values. This is known as the Median of the Distribution, which in this case is $6$ For this data, we can also determine the mean number of hours, which is $6.64$

Spread: The time span of the data ranges from $3$ to $11$ hours. By subtracting the lowest value from the greatest value, the range may be computed. $11 hours - 3 hours = 8 hours$

Outliers: The values that deviate from the main trend in some way. They do, however, stand out from the rest of the collection. In the given distribution, there is no outlier.