GCSE Statistics

GCSE Statistics

1. The Binomial Distrubution

   • expansions
     • p=1/6 chance if getting a 6.
     • q=5/6 chance of being late
       • Probability of rolling a 6?
         • p(6) = 1/6
           • • =1/6 x 1/6 x 1/6 = 1/216
           • p3 = p x p x p
         • q = 5/6
           • 3pq2 = 3x1/6 x (5/6)2
             • = 25/72
     • p= 0.4 chance of being late
     • q= 0.6 chance of being late
     • (p+q)3 = p2 + 2pq + q2
       • (p+q)3 = p3 + 3p2q + 3pq2 + q3
         • (p+q)4 = p4 + 4p3q + 6p2q2 + 4pq3 + q4
           • (p+q)5 = p5 + p5 + 5p4q + 10p3q2 + 10p2q3 + 5pq4 + q5

2. Index Numbers

   • index number for 2007: 60÷50 x 100 = 120
     • Work out the index number for each year using 2006 as the base year:
     • Index number for 2008: 65 ÷ 60 x 100 = 108.3 = 108
       • Index Number = Current Price÷base year price x 100
         • Chain Based Index Number = current price ÷ previous year price x 100
         • Weighted index number E (index number x weight) ÷ E weight
           • E = Sum
   • Simple Index numbers:

3. Time Series

   • NOTES:
     • Comment on the highest and lowest values and if there is any patterns
       • Calculate the average seasonal variation for quarter 1
         • -42 - 44 - 40 ÷ 3 = -42
     • Time is plotted on the horizontals
       • Example: The trend line for the sales of ice cream is rising, yet the sales in the first and fourth quarter are less then the trend line suggest , while those in the second and third quearters are above the trend suggesting a seasonal variation. More ice cream is sold in the summer months when weather conditions are ideal for eating ice cream.

4. Collecting Data

   • Random Sample : Where each piece of data has an equal chance of being picked.
   • Stratified Sample: Where the data sampled is in proportion to the population
   • Quota Sample: The amount of quota of each group is given eg 100 woman were sampled
   • Systematic Sampling- Data is chosen at regular intervals eg every 10th person
   • Cluster Sampling: The population is divided into groups (cluster) and then a group is chosen at random
     • Pilot survey:pre-test
       • suitable for bigger survey
   • Census: This is when all of the data in the population is taken. For example a census of the entire population of the UK is taken every 10 years.
     • Unbiased
     • Time consuming
   • Sample
     • Cheaper
     • Biased
     • Primary Data
       • Reliable
       • Time consuming
       • Secondary Data
         • Already been collected for you. Ready to analyse
         • Unreliable

5. Calculations

   • Frequency Distributions
     • Means age e.g 408 ÷ 30 = 13.6
   • Means from grouped data
     • Mean height = 1705 ÷ 15 = 113.67
   • Standard deviation

Images and files in the map