# An Introduction to Statistics by Arthur H. Hall (auth.)

By Arthur H. Hall (auth.)

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On how many buses did (a) less than 24 passengers book, (b) less than 35 book, (c) 36 or more book, (d) 40 or more book? 7. Trains arriving late on a foggy day at a London terminus: Lateness (minutes) Number of trains 1O4 208 3023 4519 6015 906 Use an ogive to find the numbers of trains late by (a) 25 minutes or more, (b) 75 minutes or more. What is (c) the 45%le and (d) the 6th decile? 8. In a certain town the monthly figures o(unemployed during the years 1960 to 1969 produced the following cumulative frequency distribution: Unemployed 200 300 400 500 or more , , , Months Unemployed Months 120 112 79 42 600 or more 700 , 800 , 16 3 2 Convert this to a percentage cumulative frequency table, draw an ogive and use it to tabulate (as in Question 5) the following: lowest decile, lower quartile, median, upper quartile, highest decile.

1 1. What are the true class limits in the following cases? (a) House prices to the nearest£ 1000 with classes £5000£8000£10000£15000-£25000 (b) Lengths of components from a factory measured to the nearest hundredth of an inch. 24. 09 31 (c) Time for soluble aspirin to dissolve in seconds. 20-23 24-27 28-31 32-35 36-39 2. The areas of a sample of farms are given to the nearest 10 acres. Calculate the mean and standard deviation. Area (acres) Number 10-90 12 100-140 8 240-280 9 150-230 13 290-510 6 520-840 4 3.

This is the modal class. Similarly the class in which the median occurs is the median class. The objection may be put that there should be more classes and that this would narrow the range in which the mode and median might be found. This however would lead to smaller frequencies in more classes, with the possible result that a single mode might not appear at all. Look at this distribution. x f I 2 2 3 3 4 4 3 5 5 6 6 7 8 2 0 9 3 II 4 13 I 16 2 The mode is 6 since this value occurs 6 times out of the total frequency of 35.

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