Statistics and Number

Statistics and Number

1. Upper and Lower Bounds

   • 1) Find the lower bound - example.. if measured to the nearest cm, take off and add on 0.5 of a cm
     • 2) Whatever you take off (i.e. 0.5) add that to find the upper bound
       • Example... A cat is measured to as 34cm to the nearest cm - what is the shortest and longest the cat could be?
         • NEAREST CM - 34-0.5 = 33.5 34+0.5=34.5

2. Estimation

   • 1) Round each of the numbers to 1 significant figure
     • 2) Work it out
       • Estimate 78.5x0.51/18.7 to prove it's close to 2.
         • 78.5 rounds up to 80. 0.51 stays the same, 0.5. 18.7 rounds up to 20.
           • therefore - 80x0.5 = 40. 40/20=2
             • A skip of sand weighs 20kg measured to the nearest kg. It is used to fill bags that will contain 250g of sand measured to the nearest 10g. WORK OUT MAXIMUM NUMBER OF BAGS THAT CAN BE FILLED
               • ALWAYS FIND UPPER AND LOWER BOUNDS OF EACH ITEM.
                 • SKIP LB - 19.5 kg (19,500 g) UB - 20.5 kg (20,500 g)
                 • BAGS LB - 245 g UP - 255 g
                 • SKIPS MAXIMUM AND BAGS MINIMUM ---> 20,500 / 245 = 83.6 BAGS (ROUND DOWN TO 83 BAGS)

3. Rounding

   • 4 or below - round down
     • 5 or above round up
       • 6.8]94 to 1 d.p. ---> next number is 9, so round up. BECOMES 6.9
         • 6.89]4 to 2 d.p ---> next number is 4, therefore number stays the same. STAYS AS 6.89
   • decimal place = first number after decimal
   • Significant Figure = first number - before and after decimal. DON'T START COUNTING SIG FIGS UNTIL THE NUMBER IS NOT A 0.
     • 41.5]111 to 3 s.f ---> next number is 1, so stays the same - 41.5
       • 41].5111 to 2 s.f ---> next number is 5, so rounds up to 42.

4. Fractions

   • Adding or Subtracting
     • AUSSIE PICNIC TABLE
       • 1/2 + 1/5 = MULTIPLY BOTTOM TOGETHER TO GET 10. 5 x 2 = 10 and 2 x 5 = 10. MULTIPLY 5 AND 1 TO GET 5. AND 2 AND 1 TO GET 2.
         • 5/10 + 2/10 = 7/10
       • 5/6 - 2/5. (6x5 = 30) (5x5=25) (2x6=12)
         • 25/30 - 12/30 = 13/30.
   • Multiplying
     • {top x top} and {bottom x bottom}
       • 2/5 x 1/3 = (2 x 1 = 2) and (5 x 3 = 15) SO FINAL ANSWER IS 2/5.
   • Dividing
     • KEEP FLIP CHANGE (KFC)
       • 2/3 / 1/3 = 2/3 x 3/1 = 6/3 = 2 BECAUSE 6 DIVIDED BY 3.