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Descriptive Statistics Study Guide 1. State whether these data are discrete or continuous. A) The heights of bonsai trees B) The shoe sizes of the All Star rugby team C) The numbers of differently colored hats on a market stall D) The weights of baby chimpanzees E) The time taken for students to write their extended essays F) The marks obtained by grade 9 in a French test G) The weights of ten pieces of sushi H) The hours of sunlight each day during the month of July I) The scores obtained when a dart is thrown 50 times J) The times taken for students in grade 11 to walk 500 m K) The number of visitors to Niagara Falls each day L) The exact weights of 100 one-kg bags of rice 2. Sixty people were asked how often they traveled by metro (underground railway) each month. The results are shown below. 26 20 10 30 80 38 62 36 46 40 14 22 4 10 20 42 6 8 76 38 30 48 68 24 38 68 12 32 50 10 4 20 10 8 48 22 60 44 16 32 42 8 28 22 6 76 16 14 44 64 56 34 46 20 8 16 74 12 16 6 A) Represent this information in a grouped frequency table B) Draw a histogram to represent the information graphically. 3. The number of hours of CAS completed in the first term for the 80 students at Idowell School is recorded below. 16 32 8 41 27 103 19 31 42 6 21 51 13 38 72 80 20 61 82 73 10 36 25 39 65 101 10 49 43 78 33 25 27 26 83 94 14 53 51 85 45 41 92 18 29 63 81 102 32 29 9 18 15 32 41 52 33 100 28 48 19 98 39 19 40 73 61 97 19 73 63 64 41 27 70 28 55 88 46 95 Represent this information in an ordered stem and leaf diagram. 4. The table shows the number of piglets in a litter. Number of piglets 6 7 8 9 10 11 12 13 14 Frequency 8 15 16 20 22 7 4 2 1 a) Find the lower quartile, the median and the upper quartile b) Draw a box and whisker plot to represent the information c) Are there any outliers? 5. Hans studied an article in Die Welt. He recorded the number of words in each sentence as shown in the frequency table. Number of Words Frequency 1–5 6 6 – 10 28 11 – 15 36 16 – 20 14 21 – 25 10 26 – 30 3 31 – 35 1 36 – 40 0 41 - 45 2 a) Draw a cumulative frequency graph to represent this information. b) Write down the lower quartile, the median, and the upper quartile. c) Given that the smallest sentence had one word and the largest had 43 words, draw a box and whiskers plot. 6. The reaction times of 50 children for catching a ruler are shown in the table. Time (s) Frequency 0≤s<1 3 1≤s<2 10 2≤s<3 14 3≤s<4 15 4≤s<5 4 5≤s<6 2 6≤s<7 1 7≤s<8 1 a) Write down the modal class b) Find an approximation for the median and mean times. 7. The mean weight of ten pineapples is 0.526 kg. Two more pineapples weighing 0.638 kg and 0.589 kg respectively are added to the other ten. Calculate the mean weight of all twelve pineapples. 8. The times taken for 30 camels to cover a distance of 10 km are given in the table. Time Taken (min) 50 ≤ s < 55 55 ≤ s < 60 60 ≤ s < 65 65 ≤ s < 70 70 ≤ s < 75 75 ≤ s < 80 80 ≤ s < 85 Frequency 2 8 10 3 4 2 1 a) Draw a cumulative frequency graph to find the interquartile range of the time taken b) Calculate an approximate value for the standard deviation of the times taken. 9. Calculate the mean and standard deviation for these data. 6 3 8 5 2 9 11 21 15 8 10. The mean of ten numbers is 5.5 4 3 a 8 7 3 9 5 8 3 A) Find the value of a B) Find the median of these numbers