LH2a
Practice - Mean, Median and Mode
TRY TO ANSWER IN TWO AND A HALF MINUTES.
QUESTIONS
QUESTIONS
1. You have the following string of numbers: 23, 18, 40, 23, 35, 19 and 28. What is the median? What is the mean? What is the mode?
2. Measures of central tendency include which of the following: a) mode, b) median, c) mean, or d) all of the above.
3. If you have a group of seven numbers, is one of the numbers the mean? Is one of the numbers the mode? Is one of the numbers the median?
4. What if the group contained eight numbers rather than seven?
5. You take three tests and score 70, 75 and 92. What is your average?
6. During an eight-day period, a business kept track of the number of new customers each day. The numbers were 6, 2, 7, 5, 4, 6, 3 and 2. What was the median number of new customers during the period?
7. What is another word for the average?
8. Your average golf score for six rounds is 81. Five of the scores are 78, 86, 82, 81 and 82. What was the score of your other round?
9. You have five numbers: 30, 26, 32, 28 and 21. What additional number could you also include to make the median of all six numbers equal to 27?
ANSWERS
1. Rearrange the numbers in order: 18, 19, 23, 23, 28, 35, and 40. The median is 23 (the second 23). The mean is (18+19+23+23+28+35+40) divided by 7, which is 186/7, or 26.57. The mode is the most frequent number, which is 23.
2. All of the above.
3. The mode is always one of the numbers, because it is the most frequent number. The median is always one of the numbers, because (in a group of odd numbers) it is the middle number. The mean is not necessarily one of the numbers.
4. The mode is still one of the numbers, as before.. But the median may not be, because in an even group of numbers the median would be the average the two middle numbers. The mean is still not necessarily one of the numbers.
5. Add the three numbers and divide by 3. 79.
6. First put the numbers in order: 2, 2, 3, 4, 5, 6, 6, and 7. The middle numbers, the fourth and the fifth out of eight, are 4 and 5. Their average is 4.5, which is the median.
7. The mean.
8. If the average of six rounds was 81, the total for all six was 81 x 6 = 486. The total of the five scores you know was 78 + 86 + 82 + 81 + 82 = 409. The other score was 486 - 409 = 77. To check, be sure that the sum of all six scores is 486.
9. The median of six numbers, in order, is the average of the third and fourth numbers. The two largest numbers of the five are 30 and 32. The two smallest numbers of the five are 21 and 26. The remaining number of the five is 26. If the average of the two middle numbers is 27, their sum is 27 x 2 = 54. One of the numbers is 26, so the other number must be 54 - 26 = 28.