Slide 1 Slide 2 Daphne Phillip Kathy Slide 3 Pick a Brick 100 pts 200 pts 500 pts 300 pts 400 pts 200 pts 300 pts 500 pts 100 pts 300 pts 400 pts 100 pts 400 pts 100 pts 200 pts 500 pts 100 pts 400 pts 5 6 7 9 10 11 12 14 15 16 18 19 20 21 23 24 25 26 27 28 29 30 200 pts 500 pts 300 pts 600 pts 300 pts 400 pts 500 pts 200 pts 600 pts
Slide 4 Find the mean, median, and mode of the data set. 3, 5, 12, 16, 7, 9, 13, 7, 8, 11 Mean = 91/10 = 9.1 3, 5, 7, 7, 8, 9, 11, 12, 13, 16 Median = (8+9)/2=8.5 Mode = 7 Slide 5 Find the mean and modal class frequency distribution. Height range Number of students 4.5 5.0 feet 25 5.0 5.5 feet 35 5.5 6 feet 20 6.0 6.5 feet 20 4.75*25 = 118.75 5.25*35 = 183.75 5.75*20 = 115 6.25*20 = 125 Mean = sum/n= 542.5/100 =5.425 Slide 6 Six test scores are given. The first 5 test scores are 15% of the final grade, and the last test score is 25% of the final grade. Find the weighted mean of the test scores. 78, 72, 86, 91, 87, 80.15(78+72+86+91+87) +.25(80) =62.1+ 20 = 82.1
Slide 7 Four test scores are given. The first 3 scores are 20% of the final grade, and the last test score is 40% of the final grade. Find the weighted mean of the test scores. 96, 85, 91, 86.20(96+85+91) +.40(86) =54.4+ 34.4 =88.8 Slide 8 Partner Identify the location of the mean, median, and mode in the distribution shown. A = mean B = median C = mode A B C Slide 9 Parnter B = mean, median, mode Identify the location of the mean, median, and mode in the distribution shown. A B C
Slide 10 In a positively skewed distribution, which is greater, the mean or the median? Mode, median, mean (mean follows the tail, positively skewed means shaped like right foot) Mean is greater. Slide 11 Partner Dormitory room prices (in dollars for one school year) for a sample of four year universities are listed. Find the sample mean and the sample standard deviation of the data. 2445, 2940, 2399, 1960, 2421, 2940, 2657, 2153, 2430, 2278, 1947, 2383, 2710, 2761, 2377 Sample mean = 2453.4 Sample standard deviation = 306.10 Slide 12 The mean rate for a satellite television from a sample of households was $49.99 per month, with a standard deviation of $2.50 per month. Between what two values do 99.7% of the data lie? (Assume bell shaped distribution) 99.7 in bellshaped (according to empirical) = mean +/ 3 sd 49.99 +/ 3(2.50) 49.99 +/ 7.50 ($42.49, $57.49)
Slide 13 The mean rate for satellite television from a sample of households was $49.50 per month, with a standard deviation of $2.75 per month. Estimate the percent of satellite television rates between $46.75 and $52.25. (Assume that the data set has a bell shaped distribution). 49.50 + k(2.75) = 52.25 K = 1 According to empirical rule, 68% of the data. Slide 14 Partner The mean of the number of sales of cars over a 3 month period is 61, and the standard deviation is 4 cars. The mean of the commissions is $1225 and the standard deviation is $573. Compare the variations to state whether sales or commissions was more consistent. Commissions was much more variable at 47% than sales at 6.6%. Slide 15 The mean length of the first 20 space shuttle flights was about 7 days, and the standard deviation was about 2 days. At least what percentage of the flights lasted between 3 and 11 days? 7 + k(2) =11 K = 2 1 (1/2 2 ) = 1.25 =.75 At least 75% of the data falls within 3 and 11 days.
Slide 16 First quartile What is the name of the position that represents the bottom 25% of the data? Slide 17 Interquartile Range What is the name of the measure that represents the middle 50% of the data? Slide 18 The weights (in pounds) of the defensive players on a high school football team are given. Make a boxand whisker plot of the data. 173 145 205 192 197 227 156 240 172 185 208 185 190 167 212 228 190 184 195 Min = 145 Q1 = 173 Median = 190 Q3 = 208 Max = 240
Slide 19 Find the Five Number summary of the data that represents the heights (in inches) of students in a statistics class below. 52 54 55 56 56 56 58 59 60 61 61 63 65 67 68 68 70 71 72 Min = 52 Q1 = 56 Median = 61 Q3 = 68 Max = 72 Slide 20 A student s test grade of 68 represents the 77 th percentile of the grades. What percent of students scored higher than 68? 100 77 = 23% scored higher Slide 21 In 2007, there were 768 oldies radio stations in the United States. If one station finds that 84 stations have a larger daily audience than it has, what percentile does this station come closest to in the daily audience ratings? 84/768 = 11% 100 11 = 89 th percentile
Slide 22 The weights of 19 high school football players have a bell shaped distribution, with a mean of 186 pounds and standard deviation of 18 pounds. Find the z scores of each player to compare which of the weights of the two football players is more unusual. A: 213 pounds B: 141 pounds A: z=1.5 B: z= 3.1 Therefore B is more unusual. Slide 23 Find the middle interquartile range in the data set represented below. IQR = Q3 Q1 = 85 50 = 35 Slide 24 Weekly salaries (in dollars) for asample of registered nurses are listed. 774, 446, 1019, 795, 908, 667, 444, 960 Justify whether there are any outliers. Which measure best describes the typical salary and why? IQR = Q3 Q1 = 934 556.5 = 377.5 Min 1.5(IQR) = 444 1.5(377.5) = 122.25 Max + 1.5 (IQR) = 1019 + 1.5(377.5) = 1010.25 Yes, 1019 > 1010.25 therefore it is an outlier. Since there is an outlier, the median (784.5) is the best measure of central tendency.
Slide 25 Partner The mean price of new homes from a sample of houses is $155,000 with a standard deviation of $15,000. The data set has a bell shaped distribution. Between what two prices do 95% of the houses fall? 95% k = 2 155000 +/ 2(15000) = (125,000, 185,000) Slide 26 Which is more useful, variance or standard deviation? Why? Standard deviation because it puts the information back into the units you were working with. Slide 27.8 minutes Find the score that represents the median of the data set.
Slide 28 A visual angle of 1.0 minutes represents which percentile according to the graph? 77 80 th percentile Slide 29 The follow represents lengths of twigs student found in inches. Find the data value that represents the 58 th percentile. 3, 5, 12, 16, 7, 9, 13, 7, 8, 11 3, 5, 7, 7, 8, 9, 11, 12, 13, 16 58(10) = 5.8 10 6 th value 9 Slide 30 The follow represents lengths of twigs student found in inches. What percentile does the value 12 represent? 3, 5, 12, 16, 7, 9, 13, 7, 8, 11 3, 5, 7, 7, 8, 9, 11, 12, 13, 16 # values below 12 = 7 (7 +.5) /10 =.75 = 75 th percentile