Maths Module1 (Data Handling)

FOR EXAMPLE

out of 618 students you must pick 40 to take part in a study about homework. to do this you must follow these steps...

STEP ONE

assign a 3 digit number from 001 to 618 to every student in the school

STEP TWO

write each number on a piece of paper and put it all into a hat and mix them up

STEP THREE

pick out 40 numbers from the hat.

FOR EXAMPLE

out of 618 students you must pick 40 to take part in a study about homework. to do this you must follow these steps...

STEP ONE

make a table (by hand or digitally) and put random numbers in any order on the table (e.g imagine a table with the numbers 7 6 5 4 3 2 1 9 8 7 5 7 8 9 4 3)

STEP TWO

you can go in any order and pick three numbers (e.g 7 6 5 4 3 2 1 9 8 7 5 7 8 9 4 3, the first number i pick would be 765, then 432, then 198)

STEP THREE

keep going till you have 40 numbers, and discard the numbers that are higher than 618 (e.g 765)

FOR EXAMPLE

out of 618 students you must pick 40 to take part in a study about homework. to do this you must follow these steps...

STEP ONE

using a scientific calculator press the shift/inv key followed by the RND key to generate three digit numbers starting from 0.001 to 0.999

STEP TWO

ignore the decimal points and read them as a whole number (e.g 0.243 = just 243)

STEP THREE

keep going till you have 40 numbers and discard the numbers that are higher than 618.

RANDOM SAMPLING.

when everyone has an equal chance of being picked.

SYSTEMATIC SAMPLING.

picking numbers in a certain order e.g 10, 20, 30, 40

CHECK FOR:

*a time limit (per day/per week etc)

*there should be a zero

*if the time over laps (if its time, numbers can overlap -decimals- ; if its whole numbers then numbers should not overlap)

The raw data is displayed together with its frequency then it is placed in suitable groups.

THE RAW DATA: 28, 43, 12, 23, 12, 17, 34, 19, 33, 49

when you are putting the numbers into the stem and leaf table remember to put the numbers in order first e.g 12, 12, 17, 19, 23, 28, 33, 34, 43, 49

STEM  (TENS)                                             LEAF (UNITS)

                               1                              |                           2,   2,   7,   9

                               2                              |                           3,   8

                               3                              |                           3,   4

                               4                              |                           3,   9                                         [KEY: 1 | 2 = 12]

NUMBER / TOTAL X SAMPLE SIZE

FOR EXAMPLE

as a part of a survery, a stratified random sample size of 60 has to be taken from students at a school. find the sample size for each year group.

YEAR 7: 156   YEAR 8: 180   YEAR 9: 224   YEAR 10: 196   YEAR 11: 210  (TOTAL: 966)

year 7: 156 / 966 x 60 = 9.689 (rounded up) = 10 students

year 8: 180 / 966 x 60 = 11.180 (rounded down) = 11 students

year 9: 224 / 966 x 60 = 13.913 (rounded up) = 14 students

year 10: 196 / 966 x 60 = 12.173 (rounded down) = 12 students

year 11: 210 / 966 x 60 = 13.043 (rounded down) = 13 students

the modal class is just the class interval with the highest frequency.

the median class interval is the class interval containing the median (middle number)

cumulative frequency means running total.

cumulative frequency diagrams are used to obtain an estimate of median and quartiles (upper, lower, inter)

to make a cumulative frequency table you must add up all the frequencys. e.g 0-10 = 7, 10-20 = 9, 20-30 = 12. the first cumulative frequency would be 7, the second would be (7+9) 16, the third would be (16+12) 28.

to plot the curve you must plot the end point of each class interval against the cumulative frequency then join the points to make a curve. (without a ruler)

WHAT TO DO IN ORDER TO WORK OUT THE: UPPER QUARTILE, LOWER QUARTILE, MEDIAN AND INTER QUARTILE RANGE.

to work out the median you must half the largest figure on the cumulative frequency graph and make a straight line until it touches the curve, then go down. (if the highest total is 60 you must make a line from 30)

to work out the lower quartile you must half the median, make a straight line until it touches the curve, then go down. (if to work out the median you use 30, then to work out the lower quartile you must use 15)

to work out the upper quartile you must add the numbers you used for the median and the lower quartile and then make a straight line from that until it touches the curve then go down. (if you've used 30 and 15 for the median and lower quartile then you must add these together to work out the upper quartile. 15+30=45 so make a line from 45 etc)

to work out the inter quartile range you must subtract the lower quartile from the upper quartile. (e.g if the upper quartile is 38 and the lower quartile is 21, then 38-21= 17 so 17 is the inter quartile range)

a frequency polygon can be drawn straight from the frequency table. you can do this by finding the midpoint of each interval and then plotting it with the frequency that is given.

THERE ARE THREE TYPES OF CORRELATION:

no correlation - when there is no pattern and the points are scattered everywhere

positive correlation - when there is a pattern which consists of the points starting from the lower left going to the upper right

negative correlation - when there is a pattern which consists of the points starting from the upper left going to the lower right

remember probability adds up to 1.

FOR EXAMPLE

a spiner has 5 coloured sides. find x

red: 0.1   ;   blue: 0.25   ;   green: 0.2   ;   orange: 0.35   ;   black: x

0.1 + 0.25 + 0.2 + 0.35 = 0.9

1 - 0.9 = 0.1

x = 0.1

FOR EXAMPLE

alan catches 30 fish from a lake and marks them. after a few days alan catches 80 fish and finds that only 18 are marked. estimate the total number of fish in the lake

30/N = 18/80  (fractions not division)

30 x 80 = 2400

2400 / 18 = 133.33333

fish are whole numbers so N = 133 fish.

you must assume that the number of fish has not increased in the few days.