Question 1170499: A class of music students kept records of the number of minutes they practised each week. This is the set of data:
60
120
150
45
70
200
160
140
120
135
155
200
45
80
110
150
140
120
110
165
185
125
145
130
110
Organize these numbers and graph the data
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Okay, let's organize and graph the music practice data.
**1. Organize the Data**
Here's the data in ascending order:
45, 45, 60, 70, 80, 110, 110, 110, 120, 120, 120, 125, 130, 135, 140, 140, 145, 150, 150, 155, 160, 165, 185, 200, 200
**2. Choose a Graph Type**
For this type of data, several graph types are suitable:
* **Histogram:** Shows the frequency distribution of the data, grouped into intervals.
* **Box Plot:** Displays the median, quartiles, and outliers of the data.
* **Dot Plot:** Shows each data point individually on a number line.
* **Stem-and-Leaf Plot:** A combination of a table and a graph that displays the data in its original form.
Let's illustrate with a histogram and a box plot, as they are commonly used for this kind of data.
**3. Histogram**
To create a histogram, we need to choose intervals (bins) for the data. Let's use intervals of 20 minutes.
* **Intervals:**
* 40-59
* 60-79
* 80-99
* 100-119
* 120-139
* 140-159
* 160-179
* 180-199
* 200-219
* **Frequencies:**
* 40-59: 2
* 60-79: 2
* 80-99: 1
* 100-119: 3
* 120-139: 5
* 140-159: 5
* 160-179: 2
* 180-199: 1
* 200-219: 2
**Histogram Description:**
The histogram would have the practice time intervals on the horizontal axis (x-axis) and the frequency (number of students) on the vertical axis (y-axis). Each bar's height represents the number of students who practiced within that interval.
**4. Box Plot**
To create a box plot, we need to find the following values:
* **Minimum:** 45
* **First Quartile (Q1):** 110
* **Median (Q2):** 130
* **Third Quartile (Q3):** 150
* **Maximum:** 200
**Box Plot Description:**
The box plot would show a box extending from Q1 to Q3, with a line marking the median. "Whiskers" extend from the box to the minimum and maximum values (or to values within 1.5 times the interquartile range, with outliers plotted as individual points).
**Key Features You'd Observe in Graphs**
* **Distribution Shape:** You can get a sense of whether the data is symmetrical, skewed, or has any clusters.
* **Central Tendency:** The median in the box plot and the peak of the histogram will give you an idea of the typical practice time.
* **Spread/Variability:** The range and interquartile range show how spread out the data is.
* **Outliers:** The box plot will clearly highlight any outliers (values that are far from the rest of the data).
I hope this helps!
Answer by ikleyn(52765)  (Show Source):
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