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March Problem of the Day Statistics: Average / Mean, Median, Mode and Range

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March 1, 2013 Each quarter, Mary’s teacher gives four tests. No test has any extra credit or bonus problems. So far, Mary’s test grades are two 85s and 89. The last test of the quarter is scheduled for next week. Can Mary obtain an “A” test average for the quarter? Explain.

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March 4, 2013 A batting average is the number of hits a batter makes, divided by the official number of at-bats he or she has had. Bases on balls and sacrifices do not count as official times at-bat. A player’s batting average is expressed by a 3-digit decimal, rounded to the nearest thousandth. What is the batting average of a player who has been to the plate 45 times, and of these times to the plate has 10 hits, 7 bases on balls and 3 sacrifices?

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March 5, 2013 A player’s on-base average is the number of times the player reaches base, divided by the number of at-bats. This includes bases on balls, being hit by a pitch, and sacrifices as at-bats. It is expressed as a 3-digit decimal, rounded to the nearest thousandth. What is the on-base average of a player who walks 5 times, singles 12 times, doubles 3 times, strikes out 5 times, grounds out 25 times, flies out 8 times and sacrifices 2 times?

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March 6, 2013 The pitcher’s performance is measured by the ERA. An earned run is a run that is not the result of a runner reaching first base or scoring because of a fielding error. A pitcher’s ERA represents the number of runs the pitcher has given up during a 9-inning game, rounded to the nearest hundredth. Calculate the ERA by multiplying the number of earned runs scored by 9, then dividing by the total number of innings pitched. Find the ERA of a pitcher who has pitched 130 ⅓ innings and has given up 50 earned runs.

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March 7, 2013 Average Rate = Total Distance ÷ Total Time A car traveled from Jackson to Smithville at an average rate of 40 mph. On the return trip along the same route, the average rate was 60 mph. If the towns are 240 miles apart, what is the average rate for the round trip?

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March 8, 2013 The range of a set of data is the difference between the greatest and least numbers in the set. The highest point on Earth is Mt. Everest at 29,028’. The lowest point is the Marianas Trench at 38,635’ below sea level. Find the range of the highest and lowest points on Earth.

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March 11, 2013 Goals are often given in ranges. A training range or target rate in beats per minute gives you the heart rate safety zone while exercising. It is based on your age and heartbeats per minute. To find your training range: (1) Start at 220 beats per minute; (2) Subtract your age; (3) Your training range is 60% to 75% of the answer from step 2. Find your training range.

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March 12, 2013 The mode is the number that occurs most often in a set of data. Depending on the set of data, there can be one mode, many modes, or no mode. Count the number of times each letter appears in the bolded sentences above. Find the mode.

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March 13, 2013 The median is the “middle” number when a set of data is arranged in numerical order. When there are two middle numbers, the median is their average. Consider the perfect squares from 1 to 25 inclusive. List the squares from lowest to highest as a set. What is the median of the set?

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March 14, 2013 A set of data may often be described by various statistical measures. Two of the most common of these measures are median and mean. The longest rivers in six of the continents are below; find the median and mean of their lengths. Volga; Europe: 2290 mi Murray; Australia: 1600 mi Yangtze; Asia: 3400 mi Nile; Africa: 3485 mi Amazon; South America: 4000 mi Mississippi; North America: 2330 mi

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March 15, 2013 The eight planets (terrestrial and gas giants) are listed below with their number of moons. Find the mode, median, and mean of the set of moons. Mercury, 0 Venus, 0 Earth, 1 Mars, 2 Jupiter, 16 Saturn, 20 Uranus, 15 Neptune, 8

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March 18, 2013 Sally earned 60, 65, 65, and 80 on four tests. How would scoring 100 on the next test affect the mean?

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March 19, 2013 In statistics, an outlier is an observation that is numerically distant from the rest of the data. Tom recorded his daily caloric intake for 5 days. The results were as follows: 2500, 2600, 2600, 2400, and How would removing the outlier affect the mean, median, and mode of the data?

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March 20, 2013 Which measure of central tendency, mean, median, or mode, would best depict information gained when analyzing the following data: 10, 200, 200, 300, 325, 351, 400?

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March 21, 2013 Adam tried to compute the average of his 7 test scores. He mistakenly divided the correct sum of all of his test scores by 6, which yielded 84 What is Adam’s correct average test score?

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March 22, 2013 A total of 50 juniors and seniors were given a math placement test. The 35 juniors attained an average score of 80 while the 15 seniors attained an average of 70. What was the average score for all 50 students who took the test?

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March 25, 2013 The heights of the members of a family are 5.8 ft, 5.9 ft, 4.3 ft, 6.1 ft, and 3.4 ft. Find the range of their heights.

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March 26, 2013 You have two test grades of 84 and 82. What must you get on the third test to have an average of 85?

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March 27, 2013 A college football team recorded attendance for its 7 home games. Find the mean, median, mode, and range. 24,329 76,875 65,312 78,698 43,243 23,416 58,704

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