Chapter 3.2

Chapter 3.2

• 1.
  Mean, Median, andMode The following data represent shoe sizes for eleven soccer players playing in a match: 43, 42, 39, 41, 41, 40, 38, 40, 40, 39, and 40 What size appears the most frequently? Arrange the sizes in order from smallest to biggest. What size is in the middle of the ordered data? Find the sum of the shoe sizes and divide the sum by 11. What is the result? Does the result show a shoe size? If it does not, explain. The mean, median, and mode are central tendency measures. Suppose we have the following data: 2, 3, 5, 7, 8, 8, and 9. 2, 3, 5, 7, 8, 8, 9 The mode is the data item that appears the most frequently 2, 3, 5, 7, 8, 8, 9 The median is the value of the middle member of a set of numbers when they are arranged in order 2+ 3+ 5+ 7+ 8+8+9=42 6 7 42 = dataofNumber valuesdataofSum =Mean What are you going to learn? to define the concepts of mean, median, and mode to calculate mean, median, and mode Key Terms: • mean • median • mode 33..22 Figure 2.4 5566 // SSttuuddeenntt’’ss BBooookk -- SSttaattiissttiiccss
• 2.
  Rate of Deathin Surabaya in 1999 Month Number January February March April May June July August September October November December 82 163 131 141 115 149 103 130 144 154 163 216 Source: Office of Civil Affairs Surabaya Figure 2.5 Find the mean, the median and the mode of the data on the right about the death rate in Surabaya in 1999. Solution a. To find the mean, find the sum of the data and then divide the sum by 12 as follows: 12 21616315414413010314911514113116382 +++++++++++ = 1691/12 = 140.9167 b. To find the median, arrange the data in order from smallest to biggest: 82, 103, 115, 130, 131, 141, 144, 149, 154, 163, 163, 216 5,142 2 144141 =+ Because the number of the data is even, the median is determined by summing the two data in the middle and then dividing the sum by 2. Therefore, the median of the data is 142.5. c. To find the mode, study the data in the table and find the data item that appears the most frequently (the value that has the highest frequency). Because number 163 appears twice, while the other numbers appear only once, therefore, the mode of the data is 163. MMaatthheemmaattiiccss ffoorr JJuunniioorr HHiigghh SScchhooooll GGrraaddee 99 // 5577
• 3.
  • Mode isthe data item with the highest frequency. • Median is the value of the middle member of a set of numbers when they are arranged in order from smallest to biggest • Mean = dataofNumber valuesdataofSum Find the mean, median, and mode of each of the following data sets: a. Scores on a mathematics test: 100, 72, 86, 86, 84, 92, 86, 90. b. Numbers of sleeping hours: 10, 8, 9, 10, 9, 9, 10, 9, 7. Solution a. The mathematics score of the 8 students: 100, 72, 86, 86, 84, 92, 86, 90. Mean = 87 8 90869284868672100 = +++++++ The mode is 86, because the score appears most frequently (3 times) in the data set. To find out the median, all the score must be put in order from the smallest to the biggest as follows: 72, 84, 86, 86, 86, 90, 92, 100. As the number of the score is even, the median is the sum of the two scores in the middle position divided by 2, that is 86 2 8686 = + . b. The numbers of sleeping hours: 10, 8, 9, 10, 9, 9, 10, 9, 7. Mean = 9 1010999109810 +++++++++ = 9 5588 // SSttuuddeenntt’’ss BBooookk -- SSttaattiissttiiccss
• 4.
  The mode is9 because the score appears most frequently (4 times) in the data set. To find out the median, all the score must be put in order from smallest to biggest as follows: 7, 8, 9, 9, 9, 9, 10,10, 10. Because the number of the score is odd, the median is the score in the middle position, that is 9. 1. Find the mean, median and mode of each of the following data sets: a. Scores on a physics test: 6, 7, 7, 8, 8, 8, 10, 10. b. The number of the male students in each class: 31, 26, 30, 35, 25, 24, 35, 30, 30, 24. 2. The following is the data that shows the ownership of domestic animals among the students in a junior high school class: 1, 0, 1, 3, 0, 2, 3, 1, 0, 6, 1, 7, 2, 1, 1, 2, 3, 0, 1, 2, 6, 2, 0, 3. a. Copy and complete the following table with the data. Number of students 1 2 3 4 5 6 7 …… Number of animals 1 0 ........ ........ ........ ......... .......... ....... b. Find out : 1). The total number of the students in the class. 2). The total number of the domestic animals. 3). The mode of the domestic animal ownership. What does it mean? 4). The mean of the domestic animal ownership. What does it mean? Country Amount Australia Canada France Germany Italy Japan Mexico Netherlands New Zealand England Others 2279 330 1703 1778 1973 2381 592 1422 2181 1596 1038 Source: World Almanac 3. The average amount of money spent by visitors in the United States (in dollar per person) is as follows: a). Find out the median of the data. What does it mean? b). Which country spent the most, and how much? c). Which countries spent more than the Netherlands? MMaatthheemmaattiiccss ffoorr JJuunniioorr HHiigghh SScchhooooll GGrraaddee 99 // 5599