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# Toán 10 Bài 3: Các số đặc trưng đo xu thế trung tâm của mẫu số liệu

Solve Math 10 Lesson 3: Feature numbers measure the central trend of the Creative Horizons data sample is an extremely useful document to help grade 10 students have more reference suggestions, easily compare results when doing math exercises from lessons 1 to 7 on pages 118, 119.

Solution for Math Textbook 10, Lesson 3, pages 118, 119 Creative horizons Volume 1 is compiled in detail, following the content in the textbook. Each problem is explained in detail. Thereby helping them consolidate and deepen the knowledge they have learned in the main program; can self-study, self-check their own learning results.

## Math Solution 10: Typical numbers measure the central trend of the data sample

• Math Solution 10 pages 118, 119 Creative horizons – Volume 1
• Lesson 1 page 118
• Lesson 2 page 118
• Lesson 3 page 118
• Lesson 4 page 118
• Lesson 5 page 118
• Lesson 6 page 119
• Lesson 7 page 119

## Math Solution 10 pages 118, 119 Creative horizons – Volume 1

### Lesson 1 page 118

Find the mean, quartile, and mode of the following data samples:

a) 23; 41; 71; 29; 48; 45; 72; 41.

b) 12; 32; ninety three; 78; 24; twelfth; 54; 66; 78.

a) 23; 41; 71; 29; 48; 45; 72; 41.

+) Average number:

+) Quartile:

Step 1: Sort the data samples in non-decreasing order:

Step 2: n = 8, is an even number, so

is the median of half the data

is the median of half the data Therefore

+) Only the value 41 appears twice, more than the rest.

b) 12; 32; ninety three; 78; 24; twelfth; 54; 66; 78.

+) Average number:

+) Quartile:

Step 1: Sort the data samples in non-decreasing order:

Step 2: n = 9, is an odd number, so

is the median of half the data

is the median of half the data

+) The value 12 and the value 78 appear twice, more than the rest.

### Lesson 2 page 118

Find the mean, quartile, and mode of the following data samples:

a) The data table is the frequency table.

The sample size is n = 6 + 8 + 10 + 6 + 4 + 3 = 37.

The sample mean is:

The value 28 has the highest frequency so the sample mode is Mo = 28.

Sorting the data samples in non-decreasing order, we get:

23; 23; 23; 23; 23; 23; 25; 25; 25; 25; 25; 25; 25; 25; 28; 28; 28; 28; 28; 28; 28; 28; 28; 28; thirty first; thirty first; thirty first; thirty first; thirty first; thirty first; 33; 33; 33; 33; 37; 37; 37.

Since the sample size is odd, the second quartile is Q .2 = 28.

The first quartile is the sample median: 23; 23; 23; 23; 23; 23; 25; 25; 25; 25; 25; 25; 25; 25; 28; 28; 28; 28. Hence Qfirst = 25.

The third quartile is the sample median: 28; 28; 28; 28; 28; thirty first; thirty first; thirty first; thirty first; thirty first; thirty first; 33; 33; 33; 33; 37; 37; 37. Hence Q3 = 31.

b) The data table is the relative frequency table.

The average is:

Relative frequency is the ratio of frequency to sample size, so the value with the highest relative frequency has the largest frequency, so the value 0 has the largest frequency so the mode of the data sample is Mo = 0.

Assuming the sample size is n = 10, then:

The frequency of the value 0 is 0.6 . 10 = 6.

The frequency of the value 2 is 0.2 . 10 = 2.

The frequency of the value 4 is 0.1 . 10 = 1.

The frequency of the value 5 is 0.1 . 10 = 1.

Sorting the data in non-decreasing order, we get:

0; 0; 0; 0; 0; 0; 2; 2; 4; 5.

Since the sample size is even, the second quartile is Q .2 = 0.

The first quartile is the sample median: 0; 0; 0; 0; 0. Hence Qfirst = 0.

The third quartile is the sample median: 0; 2; 2; 4; 5. Hence Q3 = 2.

### Lesson 3 page 118

An randomly picks 3 balls from a box containing many blue and red balls. An counts how many red balls out of the 3 taken out and returns the balls to the box. An repeated the test more than 100 times and recorded the results in the following table:

 Number of red balls 0 first 2 3 Times ten 30 40 20

Find the mean, quartile, and mode of the table above.

+) Average number:

+) Quartile:

Step 1: Sort the data samples in non-decreasing order,

Step 2: Since n = 100, is an even number, so

is the median of half the data:

is the median of half the data

+) Fashion

### Lesson 4 page 118

In a contest, people record the time to complete a product of some experiments in the following table:

 Time (unit: minutes) 5 6 7 8 35 Number of candidates first 3 5 2 first

a) Find the mean, quartile and mode of the exam time of the above candidates.

b) Last year, the test time of candidates whose mean and median were both 7. Compare the overall exam time of candidates over the two years.

a.

+) Average number:

+) Quartile:

Step 1: Sort the data samples in non-decreasing order, 5,6,6,6,7,7,7,7,7,8,8,35

Step 2: Since n = 12, is an even number, so

is the median of half the data: 5,6,6,6,7 So

is the median of half the data 7,7,7,8,8,35 So

+) Fashion

b.

+) If the average number is compared: 9.08 > 7 so the overall exam time of the candidates this year is larger than the previous year.

+) If the median is compared: The median of two years is 7 so the overall test time of candidates in two years is the same.

Because there is one candidate whose test time is much longer than the other candidates => the comparison should be based on the median.

### Lesson 5 page 118

Uncle Dung and Uncle Thu recorded the phone numbers that each person called every day for 10 days randomly selected from January 2021 in the following table:

 Uncle Dung 2 7 3 6 first 4 first 4 5 first Uncle Thu first 3 first 2 3 4 first 2 20 2

a) Find the mean, quartile, and mode of each phone number that each caller uses the above numbers

b) On average, who has more phone calls?

c) If compared by median, who has more phone calls?

d) In your opinion, should the average or the median be used to compare who has more phone calls per day?

a) Uncle Dung:

+) Average number:

+) Quartile:

Step 1: Sort the data samples in non-decreasing order, 1,1,1,2,3,4,4,5,6,7

Step 2: Since n = 10, is an even number, so

is the median of half the data: 1,1,1,2,3 So

is the median of half of the data 4,4,5,6,7 So

+) Fashion

Uncle Thu

+) Average number:

+) Quartile:

Step 1: Sort the data samples in non-decreasing order, 1,1,1,2,2,2,3,3,4,20

Step 2: Since n = 10, is an even number, so

is the median of half the data: 1,1,1,2,2 So

is the median of half the data 2,3,3,4,20 So

+) Fashion

b) Since 3.9 > 3.4, according to the average number, Mr. Thu has more phone calls.

c) Since 3.5 > 2, according to the median, Mr. Dung has more phone calls.

d) Because in the data sample, there was one day that Mr. Thu had 20 phone calls, much larger than other days, so we should compare by median.

### Lesson 6 page 119

The total number of points that the members of the International Mathematical Olympiad (IMO) team of Vietnam placed in 20 competitions are given in the following table:

 Five total score Five total score Five total score Five total score 2020 150 2015 151 2010 133 2005 143 2019 177 2014 157 2009 161 2004 196 2018 148 two thousand and thirteen 180 2008 159 2003 172 2017 155 2012 148 2007 168 2002 166 2016 151 2011 113 2006 131 2001 139

(Source: https://imo-office.org)

There is an opinion that the team’s test scores for the period 2001 – 2010 are higher than the period 2011 – 2020. Use the mean and median to check if the above opinion is correct.

+) Period 2001 – 2010

Average number

Sorting the data in non-decreasing order, we get: 131,133,139,143,159,161,166,168,172,196

Since n = 10 is even, the median is:

+) Period 2011 – 2020

Average number

Sorting the data in non-decreasing order, we get:

Since n = 10 is even, the median is:

+) Comparing by mean or median, we can see that the test scores of the 2001-2010 period are higher than the 2011-2020 period.

So the above statement is correct.

### Lesson 7 page 119

The results of the midterm test for all students in grades 10A, 10B, and 10C are listed in the charts below.

a) Make a statistic of the number of students according to their scores in each class.

b) Compare the scores of students in those grades by mean, median, and mode.

a)

 Class 10A The point 5 6 7 8 9 ten HS No first 4 5 8 14 8 Grade 10B The point 5 6 7 8 9 ten HS No 4 6 ten ten 6 4 Grade 10C The point 5 6 7 8 9 ten HS No first 3 17 11 6 2

b)

+) Class 10A

Average number

Sorting the data in non-decreasing order, we get: 5,6,6,6,6,7,7,7,7,7,

Since n = 40, is an even number, the median is:

Fashion

Average number

Sorting the data in non-decreasing order, we get:

Since n = 40, is an even number, the median is:

Fashion

Average number

Sorting the data in non-decreasing order, we get:

Since n = 40, is an even number, the median is:

Fashion

+) Compare:

Average: 8.35 > 7.6 > 7.5 => The grades of students in descending order are 10A, 10C, 10B.

Median: 9 > 7.5 > 7=> The grades of students in descending order are 10A, 10B, 10C.

Fashion: Class 10A has 14 points, Class 10B has 10 points 7 and 10 points 8, Class 10C has 17 points 7. Therefore, comparing according to fashion, the scores of classes are reduced in order: 10A, 10B, 10C

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