Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Here is a set of data. 42, 34, 47, 38, 43, 35, 40, 63, 45, 49, 41, 40, 58, 47, 45, 37 1) What is the 5-number summary for this data? 2) Construct a box-plot for this data. 3) What is the IQR? 4) Identify any outliers or explain why there are none. 5) Calculate the mean and standard deviation. 6) Comment on the shape of the distribution of data. 7) Does the relative size of the mean and median agree with what you said about the shape? Explain 8) What is the percentile rank of the number 38 in this data set? 9) What number is at the 69th percentile? 10) ACT scores have mean 21 and standard deviation 5, and the scores follow a Normal distribution. a) What percent of ACT scores are between 11 and 31? b) What percent of ACT scores are between 16 and 21? c) What percent of ACT scores are greater than 31? 42, 34, 47, 38, 43, 35, 40, 63, 45, 49, 41, 40, 58, 47, 45, 37 34, 35, 37, 38, 40, 40, 41, 42, 43, 45, 45, 47, 47, 49, 58, 63 34, 35, 37, 38 | 40, 40, 41, 42 | 43, 45, 45, 47 | 47, 49, 58, 63 39 42.5 47 1) What is the 5-number summary for this data? min = 34, Q1 = 39, med = 42.5, Q3 = 47, max = 63 2) Construct a box-plot for this data. (your box plot should have labels) 3) What is the IQR? IQR = Q3 – Q1 = 47 – 39 = 8 4) Identify any outliers or explain why there are none. Q3 + 1.5IQR = 47 + 1.5(8) = 47 + 12 = 59 Q1 – 1.5IQR = 39 – 1.5(8) = 39 – 12 = 27 63 is an outlier because it is greater than 59 5) Calculate the mean and standard deviation (34 + 35 + 37 + 38 + 40 + 40 + 41 + 42 + 43 + 45 + 45 + 47 + 47 + 49 + 58 + 63)/16 = 704/16 = 44 x 34 35 37 38 40 40 41 42 43 45 45 47 47 49 58 63 (x-µ)2 100 81 49 36 16 16 9 4 1 1 1 9 9 25 196 361 x-µ -10 -9 -7 -6 -4 -4 -3 -2 -1 1 1 3 3 5 14 19 x2 1156 1225 1369 1444 1600 1600 1681 1764 1849 2025 2025 2209 2209 2401 3364 3969 ∑ 𝑥 = 704 ∑(𝑥 − 𝜇) = 0 ∑(𝑥 − 𝜇)2 = 914 ∑ 𝑥 2 = 31890 ∑(𝑥−𝜇)2 𝜎=√ 𝑁 914 = √ 16 ∑𝑥 = 7.558 or 𝜎 = √ 2 2 −(∑ 𝑥) 𝑁 𝑁 31890− =√ (704)2 16 16 = 7.558 6) Comment on the shape of the distribution of data. Skewed right 7) Does the relative size of the mean and median agree with what you said about the shape? Explain Yes, since the distribution is skewed to the right, we expect the mean to be greater than the median, and it is! 44 > 42.5 8) 38 has 3 numbers below it (out of 16 numbers), and 3/16 = 0.1875 = 19%. So 38 is at the 19th percentile. 9) 69% of 16 numbers is about 11 numbers (11.04). So to be at the 69th percentile we need 11 numbers to be below us, so we need to be in position 12, which is the number 47. So 47 is at the 69th percentile. 10) a) 95%, b) 34%, c) 2.5%