Login
Premium
Home Question Bank Math Statistics
Question
upstudy study bank question image url

คะแนน ดังนี้ \[ \begin{array}{lllllllllllllll} 9 & 10 & 12 & 12 & 14 & 14 & 15 & 16 & 16 & 16 & 17 & 17 & 18 & 19 & 20 \end{array} \] 1. จงหาควอร์ไทล์ที่ \( 1\left(\mathrm{Q}_{1}\right) \) ควอร์ไทล์ที่ \( 2\left(\mathrm{Q}_{2}\right) \) ควอร์ไทล์ที่ \( 3\left(\mathrm{Q}_{3}\right) \) วิธีคิดตามขั้นตอน 1. หาตำแหน่งที่ จาก \( \mathrm{Q}_{\mathrm{r}}=\frac{r(N+1)}{4} \) โดยหา ตำแหน่งของ \( \mathrm{Q}_{1}, \mathrm{Q}_{2}, \mathrm{Q}_{3} \) 2. จากตำแหน่งที่หาได้ในข้อ 1 ตรงกับข้อมูลในโจทย์เท่าใด วิธีทำ

Ask by Newton Mills. in Thailand
Feb 25,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

ควอร์ไทล์ที่ 1 (Q₁) = 12, ควอร์ไทล์ที่ 2 (Q₂) = 16, ควอร์ไทล์ที่ 3 (Q₃) = 17

Solution

เรามีข้อมูลคะแนนเรียงจากน้อยไปมากดังนี้   9 10 12 12 14 14 15 16 16 16 17 17 18 19 20 จำนวนข้อมูลทั้งหมด N = 15   ขั้นตอนที่ 1: หา “ตำแหน่ง” ของ Q₁, Q₂, Q₃ โดยใช้สูตร     Qᵣ = (r (N + 1))/4                       (สำหรับ r = 1, 2, 3) 1. หาค่าตำแหน่งของ Q₁   ตำแหน่งของ Q₁ = (1×(15+1))/4 = 16/4 = 4   ดังนั้น Q₁ อยู่ที่ตำแหน่งที่ 4 ซึ่งข้อมูลตำแหน่งที่ 4 = 12   → Q₁ = 12 2. หาค่าตำแหน่งของ Q₂   ตำแหน่งของ Q₂ = (2×(15+1))/4 = 32/4 = 8   ดังนั้น Q₂ อยู่ที่ตำแหน่งที่ 8 ซึ่งข้อมูลตำแหน่งที่ 8 = 16   → Q₂ = 16 3. หาค่าตำแหน่งของ Q₃   ตำแหน่งของ Q₃ = (3×(15+1))/4 = 48/4 = 12   ดังนั้น Q₃ อยู่ที่ตำแหน่งที่ 12 ซึ่งข้อมูลตำแหน่งที่ 12 = 17   → Q₃ = 17 สรุป   Q₁ = 12  Q₂ = 16  Q₃ = 17

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg
Explain
Simplify this solution

Extra Insights

เพื่อหาควอร์ไทล์ที่ \( Q_1, Q_2, Q_3 \) เราจะทำตามขั้นตอนที่คุณกำหนดค่ะ **ขั้นตอนที่ 1: หาตำแหน่งของควอร์ไทล์** 1. จำนวนข้อมูล \( N = 15 \) (ข้อมูลทั้งหมด 15 ตัว) 2. หาตำแหน่งของ \( Q_1 \): \[ Q_1 = \frac{1(15+1)}{4} = \frac{16}{4} = 4 \] 3. หาตำแหน่งของ \( Q_2 \): \[ Q_2 = \frac{2(15+1)}{4} = \frac{32}{4} = 8 \] 4. หาตำแหน่งของ \( Q_3 \): \[ Q_3 = \frac{3(15+1)}{4} = \frac{48}{4} = 12 \] **ขั้นตอนที่ 2: เช็คค่าที่ตำแหน่งที่หามา** - สำหรับ \( Q_1 \) ที่ตำแหน่งที่ 4 จะได้ค่า = 12 - สำหรับ \( Q_2 \) ที่ตำแหน่งที่ 8 จะได้ค่า = 16 - สำหรับ \( Q_3 \) ที่ตำแหน่งที่ 12 จะได้ค่า = 17 ดังนั้น ค่าของควอร์ไทล์จะเป็น: - \( Q_1 = 12 \) - \( Q_2 = 16 \) - \( Q_3 = 17 \)

Related Questions

Quiz Active TIME REMAINING Zachary completes a hypothesis test and finds that he rejects the null hypothesis. Which statement gives a reason for rejecting the null hypothesis? The \( z \)-statistic is less than 0 . The \( z \)-statistic lies in the critical region. The \( z \)-statistic lies outside the critical region. The \( z \)-statistic is greater than 0 .
Statistics United States Feb 25, 2025
The College Board states that the average math SAT score is 514 with a standard deviation of 117 . Colleen gathered data from 50 students in her graduating class and found the average score to be 523 . She thinks that her class's math SAT score is different from the average. Which of the following are the correct null hypothesis and alternate hypothesis? \( \mathrm{H}_{0}: \mu=514 ; \mathrm{H}_{\mathrm{a}}: \mu>514 \) \( \mathrm{H}_{0}: \mu=514 ; \mathrm{H}_{\mathrm{a}}: \mu=523 \) \( \mathrm{H}_{0}: \mu=514 ; \mathrm{H}_{\mathrm{a}}: \mu=514 \) \( \mathrm{H}_{0}: \mu=514 ; \mathrm{H}_{\mathrm{a}}: \mu=523 \)
Statistics United States Feb 25, 2025
1 TIMEREMAINING \( 46: 43 \) Julian is a manager at a clothing store for teens. He is analyzing the order for next seas̈on. Data for the previous 10 years suggests that teens are willing to spend an average of \( \$ 75 \) for a pair of designer jeans with a standard deviation of \( \$ 5 \). However, Julian thinks the average may have changed due to a recession. He finds that the last three seasons of data show that teens spent an average of \( \$ 68 \) on a pair of jeans. Therefore, he performed a hypothesis test to see if the recent average is the same. Julian used a significance level of \( 5 \% \) to perform the test. Which of the following statements is valid based on the results? Julian's data shows that the recent seasons' average jean price is not \( \$ 75 \). Julian's data shows that he should order fewer jeans than before. Julian's data shows that the recent seasons' average jean price is still \( \$ 75 \). Julian's data is inconclusive, so he should order the same number of jeans.
Statistics United States Feb 25, 2025
12 A recent survey of 8,000 high school students found that the mean price of a prom dress was \( \$ 195.00 \) with a standard deviation of \( \$ 12.00 \). Alyssa thinks that her school is more fashion conscious and spent more than \( \$ 195.00 \). She collected data from 20 people in her high school and found that the average price spent on a prom dress was \( \$ 208.00 \). Which of the following is the correct \( z \)-statistic for this situation? 0.24 4.84 7.51 96.90
Statistics United States Feb 25, 2025
1 TIMEREMAINING A recent survey of 8,000 high school students found that the mean price of a prom dress was \( \$ 195.00 \) with a standard deviation of \( \$ 12.00 \). Alyssa thinks that her school is more fashion conscious and spent more than \( \$ 195.00 \). She collected data from 20 people in her high school and found that the average price spent on a prom dress was \( \$ 208.00 \). Which of the following is the correct \( z \)-statistic for this situation? 0.24 4.84 7.51 96.90
Statistics United States Feb 25, 2025

Latest Statistics Questions

1 2 3 4 5 6 7 8 9 TIME REMAINING 41:29 Dion is performing a hypothesis test in which the population mean is 92 and the standard deviation is 2 . His sample size is 7 with a mean of 93.5 . Which of the following correctly depicts the \( z \)-statistic for this data? 0.28 0.36 1.98 2.63
Statistics United States Feb 25, 2025
1 2 4 TMEREMANING David wants to complete a hypothesis test with the least amount of probability for error. If he sets the significance level to \( 1 \% \), assuming his sample is truly random, what else could he adjust in the test in order to reduce error? He could change the population mean. He could increase the sample size. He could change the population standard deviation. He could decrease the sample size.
Statistics United States Feb 25, 2025
A study investigated the job satisfaction of teachers allowed to choose supplementary cैurriculum for their classes versus teachers who were assigned all curricular resources for use in their classes. On average, when surveyed regarding job satisfaction, teachers give a score of 3.3 out of 5 with a standard deviation of 0.6 . When the authors of the study interviewed 40 teachers who supplemented with their own materials, they found 3.5 to be the mean. The authors wanted to know if the group of teachers that could choose supplementary curriculum had a higher level of job satisfaction. They used a significance level of \( 1 \% \). Which of the following statements is valid based on the results of the test? The data shows that teachers allowed to choose supplementary curriculum for classes are more satisfied with their jobs. The data shows that teachers who were assigned all curricular resources for classes are more satisfied with their jobs. The data shows that there is no difference in job satisfaction between the two groups of teachers. The data shows that the authors cannot make a determination either way with this data.
Statistics United States Feb 25, 2025
1 TIMEREMAINING \( 46: 43 \) Julian is a manager at a clothing store for teens. He is analyzing the order for next seas̈on. Data for the previous 10 years suggests that teens are willing to spend an average of \( \$ 75 \) for a pair of designer jeans with a standard deviation of \( \$ 5 \). However, Julian thinks the average may have changed due to a recession. He finds that the last three seasons of data show that teens spent an average of \( \$ 68 \) on a pair of jeans. Therefore, he performed a hypothesis test to see if the recent average is the same. Julian used a significance level of \( 5 \% \) to perform the test. Which of the following statements is valid based on the results? Julian's data shows that the recent seasons' average jean price is not \( \$ 75 \). Julian's data shows that he should order fewer jeans than before. Julian's data shows that the recent seasons' average jean price is still \( \$ 75 \). Julian's data is inconclusive, so he should order the same number of jeans.
Statistics United States Feb 25, 2025
1 TIMEREMAINING \( 49: 59 \) A researcher collated data on Americans' leisure time activities. She found the mean nümber of hours spent watching television each weekday to be 2.7 hours with a standard deviation of 0.2 hours. Jonathan believes that his football team buddies watch less television than the average American. He gathered data from 40 football teammates and found the mean to be 2.3. Which of the following are the correct null and alternate hypotheses? \( \mathrm{H}_{0}: \mu=2.7 ; \mathrm{H}_{\mathrm{a}}: \mu<2.7 \) \( \mathrm{H}_{0}: \mu \neq 2.7 ; \mathrm{H}_{\mathrm{a}}: \mu=2.3 \) \( \mathrm{H}_{0}: \mu=2.7 ; \mathrm{H}_{\mathrm{a}}: \mu \neq 2.7 \) \( \mathrm{H}_{0}: \mu<2.7 ; \mathrm{H}_{\mathrm{a}}: \mu \geq 2.3 \)
Statistics United States Feb 25, 2025
Prev Next
Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy