Question

mode
example #2
the following data show the distances (in miles) from the homes of off - campus statistics
students to the college.
0.5; 0.7; 1.1; 1.2; 1.2; 1.3; 1.3; 1.5; 1.5; 1.7; 1.7; 1.8; 1.9; 2.0; 2.2; 2.5; 2.6; 2.8; 2.8; 2.8;
3.5; 3.8; 4.4; 4.8; 4.9; 5.2; 5.5; 5.7; 5.8; 8.0
stem and leaf graph:
mode __________ median ________ mean __________

Explanation:

Step1: Find the mode

The mode is the number that appears most frequently. In the data set, \(2.8\) appears \(3\) times.

Step2: Find the median

First, count the number of data points \(n = 30\). Since \(n\) is even, the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+ 1)\)th values. \(\frac{n}{2}=15\), \(\frac{n}{2}+1 = 16\). The 15th value is \(2.2\) and the 16th value is \(2.5\). Median \(=\frac{2.2 + 2.5}{2}=\frac{4.7}{2}=2.35\)

Step3: Find the mean

Sum of all data points:

$$
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Mean \(=\frac{86.7}{30}=2.89\)

Answer:

Mode: \(2.8\), Median: \(2.35\), Mean: \(2.89\)