Question

practice
example 1
find the mean, median, and mode for each data set.

1. (17, 11, 8, 15, 28, 20, 10, 16)
2. (2.5, 6.4, 7.0, 5.3, 11, 6.4, 3.5, 6.2, 3.9, 4.0)

3.

1	2
1	4
5	6
7	2

4.

30	80	60	90
10	30	110	70

1. number of students helping at a booth each hour: 3, 5, 8, 1, 4, 11, 3
2. weight in pounds of boxes loaded onto a semi - truck: 201, 201, 200, 199, 199
3. car speeds in miles per hour observed by a highway patrol officer: 60, 53, 53, 52, 53, 55, 55, 57
4. number of songs downloaded by students last week in ms. turner’s class: 3, 1, 7, 21, 23, 63, 27, 29, 95, 23
5. ratings of an online video: 2, 5, 3.5, 4, 4.5, 1, 1, 4, 2, 1.5, 2.5, 2, 3, 3.5

Explanation:

Let's solve problem 1: Find the mean, median, and mode for the data set (17, 11, 8, 15, 28, 20, 10, 16).

Step 1: Find the Mean

The mean is calculated by summing all the values and dividing by the number of values.
First, sum the data: \(17 + 11 + 8 + 15 + 28 + 20 + 10 + 16\)
\(= (17+11)+(8+15)+(28+20)+(10+16)\)
\(= 28 + 23 + 48 + 26\)
\(= 28+23 = 51\); \(48+26 = 74\); \(51 + 74 = 125\)
Number of values \(n = 8\)
Mean \(= \frac{125}{8} = 15.625\)

Step 2: Find the Median

First, order the data set from least to greatest: \(8, 10, 11, 15, 16, 17, 20, 28\)
Since \(n = 8\) (even), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values.
\(\frac{n}{2} = 4\), \(\frac{n}{2}+1 = 5\)
4th value: \(15\), 5th value: \(16\)
Median \(= \frac{15 + 16}{2} = \frac{31}{2} = 15.5\)

Step 3: Find the Mode

The mode is the value that appears most frequently. In this data set, all values appear once, so there is no mode (or we can say all values are modes with frequency 1). But typically, if no value repeats, we state there is no mode.

Final Answers:

• Mean: \(15.625\)
• Median: \(15.5\)
• Mode: No mode (all values occur once)

Answer:

Let's solve problem 1: Find the mean, median, and mode for the data set (17, 11, 8, 15, 28, 20, 10, 16).

Step 1: Find the Mean

The mean is calculated by summing all the values and dividing by the number of values.
First, sum the data: \(17 + 11 + 8 + 15 + 28 + 20 + 10 + 16\)
\(= (17+11)+(8+15)+(28+20)+(10+16)\)
\(= 28 + 23 + 48 + 26\)
\(= 28+23 = 51\); \(48+26 = 74\); \(51 + 74 = 125\)
Number of values \(n = 8\)
Mean \(= \frac{125}{8} = 15.625\)

Step 2: Find the Median

First, order the data set from least to greatest: \(8, 10, 11, 15, 16, 17, 20, 28\)
Since \(n = 8\) (even), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values.
\(\frac{n}{2} = 4\), \(\frac{n}{2}+1 = 5\)
4th value: \(15\), 5th value: \(16\)
Median \(= \frac{15 + 16}{2} = \frac{31}{2} = 15.5\)

Step 3: Find the Mode

The mode is the value that appears most frequently. In this data set, all values appear once, so there is no mode (or we can say all values are modes with frequency 1). But typically, if no value repeats, we state there is no mode.

Final Answers:

• Mean: \(15.625\)
• Median: \(15.5\)
• Mode: No mode (all values occur once)