Answer: d. 100.
The mean acts as a balancing point for the values in a data set. Since all the numbers in this set are less than 50, and the mean is 50, the missing value must be greater than 50. This means that you can quickly eliminate the three answers that are 50 or less. If you did not notice this, you could still compute the missing value. Since there are four values in the data set, they must all add up to 50 * 4 = 200. Subtract the three known values from 200 to get the unknown value: 200 – 20 – 30 – 50 = 100.
Answer: d. 25.
The median is the "middle" value of the data set, so the first thing you must do is reorder the values so they are in ascending order: {10, 20, 30, 40}. If the data set had an odd number of values, the median would be the middle one, but in this case, the data set has an even number of values. Therefore, you need to take the number half way between the middle two values: 20 and 30. The middle value between 20 and 30 can be found by averaging the two values: (20 + 30) / 2 = 50 / 2 = 25. The median of this set is therefore 25.
Answer: b. {40, 10, 20, 50}
The range is the difference between the highest value and the lowest value. For set "b", that is 50 – 10 = 40.
Answer: a. {30, 50, 10, 20, 30, 40, 50}.
To find the number of modes in a given data set, find the value that occurs most often. If there is a "tie", then there is more than one mode, unless every data value occurs the same number of times, in which case there is no mode. Set "a" has one of each value except for 30 and 50, which each occur twice. Therefore, set "a" has two modes: 30 and 50. Set "b" has only one mode: 70 (because 70 is the only value that occurs more than once), and set "c" has only one mode: 30 (because 30 is the only value that occurs more than twice). Set "d" has no mode because every value occurs the same number of times.