Statistics

1. Statistics

2. Mode: the most common number.The number with the highest frequency. • A) consider the following numbers. • 24,22,20,22,23,25,23,23,26 • The most common number is 23. • Therefore mode or modal number is 23 • B) Consider the following numbers . • 15,28,19,19, 18,15,20 • There are two numbers which are more common • Therefore mode or modal numbers are 15 and 19.

3. Median : The number in the middle • A) Consider the following set of numbers • 5,7,3,4,9,3,8 • Put the numbers in order • 3,3,4,5,7,8,9 • Cross out from each side until you are left with a number in the middle • Median is 5 • B) consider the following set already in order • 23,24,24,27,28,29 • If there are two numbers in the middle, add them up and divide by 2 • (24+27) /2 = 25.5

4. Mean ( also known as average) • Consider the following set of numbers. • 24,42,35,63,36 • Average = total ÷ number • Average = ( 24 + 42 + 35 + 63 + 36) ÷ 5 = 200 ÷ 5 = 40

5. Range : largest - smallest • Consider the following set of numbers • 67,90, 22, 45, 35, 83 • Range = largest - smallest • Range = 90 – 22 = 68 • IMPORTANT : if the values have units, then the mode, median, range and mean have units as well.

6. WORD PROBLEMS INVOLVING AVERAGES • The average of my three tests is 85. If I get 95 in my next test, what will my average be ? • You cannot work directly with average, so can only work with totals. • The total for my three tests was 85 x 3 = 255 • The total for my four tests is now 255 + 95 = 350 • So my new average is total ÷ number • Average = 350 ÷ 4 = 87.5

7. More word problems • The average number of hours I worked from Monday to Thursday was 8.5h per day. The average number of hours I worked from Monday to Friday was 8.7h per day. How many hours did I work on Friday? • You cannot work directly with averages, so can only work with totals. • Total number of hours Mon to Thurs = 8.5 x 4 = 34 h • Total number of hours Mon to Fri = 8.7 x 5 = 43.5h • The difference between them is how much I worked on Friday. • Therefore on Friday I worked 43.5 – 34 = 9.h hours

8. Practice problems • Clayton plays basketball on a team. He has played three games so far. In the first game, he scored 10 points. In the second game, he scored 14 points. In the third game, he scored 6 points. What is Clayton's average points per game? • answer: 10 points • Harley read 5 books in January, 8 books in February, 4 books in March, and 7 books in April. What is the average number of books Harley read per month? • answer: 6 books

9. More practice • When a number x is added to the set of numbers 5, 7, 8, 12, 6, 10 and 11; the new mean is 9. Calculate the value of x.  • The mean height of the 30 children in a room is 76 cm. James, whose height is 107 cm went into the room. What is the new mean of the height of the children in the room? • The mean of a set of 10 numbers is 60. When a number x is added to the set, the mean is changed to 65. Find the value of x. • The mean weight of a group of 15 athletes was 60 kg. Two athletes whose weights were 68kg and 65 kg left the group.What is the new mean weight of the remaining athletes in the group?

10. Answers • 13 • 77cm • 115 • 59kg