March 2014Problem of the Day

Statistics: Average / Mean, Median, Mode and Range

March 3, 2014 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.

March 4, 2014 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?

March 5, 2014 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?

March 6, 2014 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.

March 7, 2014Average 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? Why do we have to use an average rate?

March 10, 2014 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. Explain how range is used in your program or another example.

March 11, 2014 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. Why do you need this information?

March 12, 2014 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.

How is finding the mode of a set of data useful?

March 13, 2014 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? How is finding the median of a set of data useful?

March 14, 2014 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 and explain the process.

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

March 17, 2014 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. Which statistical measure is the most useful in this example and why?

Mercury, 0 Venus, 0 Earth, 1 Mars, 2

Jupiter, 16 Saturn, 20 Uranus, 15 Neptune, 8

March 18, 2014 Sally earned 60, 65, 65, and 80 on four

tests. How would scoring 100 on the next test affect the mean? Explain why you would want to know how your grades are calculated. How would you use this knowledge?

March 19, 2014 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 3900. How would removing the outlier affect the mean, median, and mode of the data? Why would you want to remove outliers from a data set?

March 20, 2014 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? Describe a situation where you would get data values like this. Does that change the statistical measure that you chose?

March 21, 2014 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? Why would you want to keep track of your test scores? What would you do with that information?

March 24, 2014 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? Why do colleges and universities give placement tests?

March 25, 2014 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. Why do medical professionals collect family health information? Give an example to illustrate your reason.

March 26, 2014 You have two test grades of 84 and 82.

What must you get on the third test to have an average of 85? Give an example of why you would want to have a particular grade point average.

March 27, 2014 A college football team recorded attendance for

its 7 home games. Find the mean, median, mode, and range. How do you think the school might use this data?

24,329 76,875 65,312 78,698 43,243 23,416 58,704

March 28, 2014Would you use mean, median, mode, or

range for each situation? 1. Jack noticed that half of the cereal brands in the

store cost more than $2.00.2. The average score on the last test was 77.3. The most common height on the basketball

team is 6 ft 1 in.4. The heights of players on the basketball team

vary by 8 inches.

How could you use the statistical measure information you calculate to make a predication about the future?

March 31, 2014 In statistics, an outlier is an observation

that is numerically distant from the rest of the data. What effect will the outlier have on the median of the data if the outlier is excluded?64, 56, 59, 125, 58, 64, 65

Describe a situation where an outlier changes your interpretation of the data.