Question

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

1. {13, 11, 8, 19, 28, 20, 16, 10}
2. 2.8, 6.4, 7.0, 5.3, 1.1, 6.4, 3.5, 6.2, 3.8, 4.0
3. (chart with numbers)
4. (chart with numbers)
5. number of students helping at a booth each hour: 3, 5, 8, 1, 4, 11, 3
6. weight in pounds of boxes loaded onto a semi - truck: 201, 201, 200, 198, 199
7. car speeds in miles per hour observed by a highway patrol officer: 60, 53, 53, 52, 53, 58, 58, 57
8. number of songs downloaded by students last week in ms. turner’s class: 3, 7, 21, 23, 63, 27, 29, 95, 23
9. ratings of an online video: 2, 5, 3.5, 4, 4.5, 1, 1, 4, 2, 1.5, 2.5, 2, 3, 3.5

example 2
marching band a competition was recently held for 12 high school marching bands. each band received a score from 0 through 100, with 100 being the highest.
(chart with band and score: freeport 78, ross 85, hamilton 88, groveport 94, lakehurst 56, benton 77, madison 69, monmouth 67, carlisle 65, dupont 48, cave city 90, monroe 80)

1. find hamilton high school’s percentile rank.
2. find monmouth high school’s percentile rank.
3. find freeport high school’s percentile rank.

mixed exercises

1. reasoning the mean number of people at the movies on saturday nights throughout the year is 425, and the median is 412. explain why the mean could be slightly higher.
2. reasoning the mode length of time it takes to fly from new york city to chicago is 2 hours 35 minutes, and the mean is 3 hours 15 minutes. explain why the mode could be slightly lower.

Explanation:

Let's solve problem 1 first: finding the mean, median, and mode for the data set {13, 11, 8, 19, 28, 20, 16, 10}.

Step 1: Find the Mean

The mean is the sum of all values divided by the number of values. First, sum the data: \(13 + 11 + 8 + 19 + 28 + 20 + 16 + 10\). Let's calculate that: \(13+11=24\), \(24+8=32\), \(32+19=51\), \(51+28=79\), \(79+20=99\), \(99+16=115\), \(115+10=125\). There are 8 values, so the mean is \(\frac{125}{8} = 15.625\).

Step 2: Find the Median

First, order the data set from least to greatest: {8, 10, 11, 13, 16, 19, 20, 28}. Since there are 8 (an even number) values, the median is the average of the 4th and 5th values. The 4th value is 13, the 5th is 16. So median is \(\frac{13 + 16}{2} = \frac{29}{2} = 14.5\).

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 say no mode).

Answer:

• Mean: \(15.625\)
• Median: \(14.5\)
• Mode: No mode (all values occur once)