WorkSHEET 13.3 Univariate data II Name:

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1 WorkSHEET 13.3 Univariate data II Name: 1 The back-to-back stem-and-leaf plot shows the number of people (to the nearest thousand) that attend cricket matches in both Sydney and Melbourne during a season. Key Sydney Melbourne Leaf Stem Leaf (a) Calculate median attendance at cricket matches in both Sydney and Melbourne. (b) Calculate the range of attendance in both cities. (c) Comment on the distribution in each case. (a) Sydney median Melbourne median (b) Sydney range Melbourne range (c) Although the median attendance in both cities is approximately equal, there is a greater range of attendance in Melbourne. Twenty golfers play a round of golf on both Saturday and Sunday. Their scores are shown below: Saturday: Sunday: (a) Display these results in a back-to-back stem-and-leaf plot. (b) Comment on the distribution of each data set and give a possible reason for the differences. (a) Key Saturday Sunday Leaf Stem Leaf (b) On Sunday the scores were generally higher. This may have been caused by wind or rain making it harder to play golf. John Wiley & Sons Australia, Ltd Page 1

2 3 The data shown on the box-and-whisker plot below compares the number of cans of Coke and Pepsi sold at a corner store each day. (a) Coke median 76 Pepsi median 70 (b) Coke range Pepsi range (a) For each item state the median. (b) For each item state the range. (c) For each item find the interquartile range. (c) Coke IQR Pepsi IQR In the figure below: (a) Are the data symmetrical? (b) What is the mode(s)? (c) Can you find the mean and median? (a) No, the data are not symmetrical. (b) Mode 18 (c) The mean and median cannot be seen from the graph but could be calculated. 5 The figure below shows the results on an exam by all Year 10 students. (a) Are the data symmetrical? (b) What is the modal class? (c) Describe the skewness of the data. (a) No, the data are not symmetrical. (b) Modal class The data are negatively skewed. John Wiley & Sons Australia, Ltd Page

3 6 The data in the back-to-back stem-and-leaf plot below show the number of visitors that attends a small museum on weekdays and on weekends Key Weekdays Weekends Leaf Stem Leaf (a) Find the median of each data set. (b) Find the range of each data set. (c) Find the interquartile range of the data set. (d) Display the results on parallel box-andwhisker plots. Continued... 10th +11th scores (a) Weekday median th + 6th scores Weekend median (b) Weekday range Weekend range th + 6th scores (c) Weekday Q th +16th scores Weekday Q IQR Weekend Q1 3rd score Q3 8th score IQR (d) John Wiley & Sons Australia, Ltd Page 3

4 7 Consider the data shown in the two diagrams below. (a) Both data sets are symmetrical. (a) State whether each data set is symmetrical. If the data set is not symmetrical, state whether it is positively or negatively skewed. (b) For each data set, state the mode(s). (c) Can you see the mean for each data set? (d) For which data set will the standard deviation be greater? (b) Data set 1: Mode 3 Data set : Mode 1 and 5 (c) For both data sets the mean is 3. (d) The standard deviation will be greater for Data set as more scores are spread further from the mean. John Wiley & Sons Australia, Ltd Page 4

5 8 The organisers of a surf contest examine two beaches where they would consider holding the contest. Each day for two weeks they record the height of the surf (in metres). Beach A: 1., 1.5, 1.6, 1.3, 1.8, 1.4, 1.6, 1.3, 1.4, 1.8, 1.5, 1.4, 1.1, 1.0 Beach B: 0.9,.3, 0.7, 1.8,.3, 0.4, , 1.9,.,.4, 1.8, 1.0,.3 (a) Find the mean height of the surf each day. (b) Find the standard deviation of the surf height at each beach. (c) The organisers would like the greatest height possible, but a minimum height of 1. metres is required for the surf contest. Which beach would you recommend? (a) Beach A: x 1.4 Beach B: x 1.53 (b) Beach A: s 0.3 Beach B :s 0.74 (c) 5NS Beach A Beach B Although the mean height is greater at Beach B, the greater Standard Deviation means Beach B is less dependable. Considering the 5NS, you will note that for three quarters of the days measured Beach A had surf that was big enough to hold the contest, whereas Beach B had surf too small to hold the contest on half of the days recorded. I would therefore recommend that the surf contest be held at Beach A. 9 Calculate the 5-number summary values for the mid-semester and end-semester test results for the 15 students in the table below. Student Mid-sem. % End-sem. % Mid -semester Lowest score 7% Q 39% 1 Median 58% Q % Highest score 90% End -semester Lowest score 0% Q 4% Median 60% Q 75% Highest score 9% John Wiley & Sons Australia, Ltd Page 5

6 10 The following stem-and-leaf plot represents the scores of a cricketer: Key Stem Leaf The box plot representing this data is shown below. Using the stem-and-leaf plot, find the range and the IQR for the data. 3 pieces of data Median is the 1th piece of data in order 41 Q1 16 Q3 78 Lowest score 0 Lower quartile 16 Median 41 Upper quartile 78 Highest score 99 The box plot is a true representation of the stem-and-leaf plot. Verify that the box plot is a true representation of the stem-and-leaf plot. John Wiley & Sons Australia, Ltd Page 6

7 11 A large block of land had an old cottage situated in one corner. The land was subdivided into six smaller blocks of land with the cottage sitting on one of them. The cottage was valued at $ New houses were built on the other five blocks of land and they were valued at $ , $ , $ , $ and $ The value of the cottage would be regarded as an outlier compared with the values of the other five houses. (a) (b) (c) Considering only the values of the five new houses, calculate the: (i) mean (ii) median (iii) mode. Including the value of the cottage, calculate the: (i) mean (ii) median (iii) mode. Comment on the effect the outlier has on these three measures. (a) (i) Mean x å å $ (ii) Median middle score $ (iii) Mode most frequent score (b) (i) Mean x $ As can be seen from the table above, the inclusion of the value of the cottage has caused the mean to drop almost $ The median has only dropped $7500 and the modal value has not been affected by the outlier. å å x f $ (ii) Median middle score $ (iii) Mode most frequent score x f $ houses 6 houses Mean $ $ Median $ $ Mode $ $ John Wiley & Sons Australia, Ltd Page 7

Solutionbank S1 Edexcel AS and A Level Modular Mathematics

Solutionbank S1 Edexcel AS and A Level Modular Mathematics Page 1 of 1 Exercise A, Question 1 A group of thirty college students was asked how many DVDs they had in their collection. The results are as follows. 12 25 34 17 12 18 29 34 45 6 15 9 25 23 29 22 20