Data management Drawing circle graphs Histogram

N8-U5-L5 Shape of data

N8- U5- L3 Central tendency

N8- U5- L4 Surveys: Relating census and sample

lesson N8- U5- L1 By: Christy Au-Yeung Data management There are many types of graphs and which can be used to display the data. Some graphs are better to display a certain type of data then others.

Central tendency is the number that best represents the middle. It can be measured by median, mode or mean. Some types of measures of central tendancy can better describe the data than others For example Jane wants to know if the students in her class prefer vanilla or chocolate ice cream Jane If Jane is asking her whole class then it is called a census survey in other words a census survey is asking the whole population Which type of ice cream do you prefer: vanilla or chocolate? But, if Jane only asked 2 people in her class this question it would be considered a sample survey In other words if you only ask a part of the population (in this case the population of the class) it is called sample survey. Sample surveys are faster but could lead to inaccurate answers, for example if Jane asked her class "which gender is better, boys or girls" and she only asked the girls the obvious answer would be.....

Girls but if she asked her whole class it could lead to a different answer. If Jane directly asked the question to her class then it is called primary data, that is when you collect the answers yourself. If Jane found out if people prefer chocolate or vanilla ice cream online, on the news.... it is called secondary data. It is when you dont collect the data yourself.

Other sources of secondary data are...

- The internet

- Online

- From a book The information she gets from her class would be considered as primary data since she collected it herself. There is also.....

- qualative data: information collected can be described as ideas/ words like favourite movie or favourite flavour of ice cream

- discrete data: information collected can be described in whole numbers for example, there are 2 boys in a class

- continuous data: information collected can be described in fractions or decimal numbers, how tall all the students grew in a year Median: middle of the numbers when arranged in ascending or descending order 1. Arrange in ascending/ descending order 1, 2, 3, 4, 5 2. Find the number in the middle 1, 2, 3, 4, 5 3 is the median of this set of data Mode: the number that repeats the most

NOTE: there could be no mode,

or more than one mode 1,1,2,3,4 in this set of data 1 is the mode Mean: when you add all the numbers together than divide by the number of numbers Set of data: 1,2,3,4,5 1. Add all the numbers together

1+2+3+4+5= 15

2. Divide the result you got in the first

step by the number of numbers, in this

case 5

15/ 5= 3

The mean is 3 Circle graph Used for data that are parts of a whole, in this example it shows the whole week.

Some other examples are: shoes in family closet, slices of pizza each person ate Line graph Displays data that changes over time Some other examples are: the height of a student each month Bar graph Displays data that can be counted Double bar graphs are used when there are 2 sets of data Data can be misinterpreted by the scale A histogram is similar to a bar graph in structure except it shows how frequently the data occurs in appropriate intervals. Notice how in the histogram there are no spaces between the bars The scale is in intervals How to draw a histogram 1.Arrange the data in numerical order and group them in to equal intervals * the pieces of data in the interval is called the frequency 2. Use the horizontal axis to represent the intervals and the height represents the frequency of the intervals. * or you can use the vertical axis as intervals and horizontal as frequency) REMEMBER.... there are no spaces between the bars Number of children who visited the zoo Age group

6-7

7-8

8-9

9-10 Frequency

75

50

25

100 1. 2. Outliers A number in a set which is different and far apart from the other numbers. When you take away the outlier while finding the central tendancy, the answer will be more accurate. 1,2,3,4,10 Central tendancy

with outlier Central tendancy

without outlier Mode: none

Median: 3

Mean: 4 Mode: none

Median: 2.5

Mean: 2 The central tendancy which is the least affected by the outlier is the best describer (excluding mode, the mode ris mostlyt used for describing measures, such as sizes)

In this case the median is the best describer Look how the outlier affected the central tendancy, when there is more data, the outlier affects the central tendancy even more Favourite fruit Number of students

Banana 8

Apple 7

Peach 12

Grape 15 This is the data Correctly interpreted Misinterpreted In this chart, it makes it seem like grapes are a lot more popular than apples, but in reality, they actually arent Notice the difference in the scale.

Companies can misinterpret data to better sell their products or company How to change data to percentages: Fruits Students who ate

Banana 2

Apple 1

Peach 3

Pear 4 1. Find the total: 2+1+3+4= 10 students

2. Write a fraction for each topic

(fruits in this case)

Banana: 2/10 Apple: 1/10 Peach: 3/10 Pear: 4/10

3. To change a fraction into percentage multiply each fraction by 100%

Banana: 2/10 x 100= 20% Peach: 3/10 x 100= 30%

Apple: 1/10 x 100 = 10% Pear: 4/ 10 x 100= 40%

To change into a degree out of 360 (for the circle) multiply the fraction by 360

Banana: 2/10 x 360= 72 Peach: 3/10 x 360= 108

Apple: 1/10 x 360= 36 Pear: 4/ 10 x 360= 144 How to draw your percentages onto the circle graph:

1. Draw a circle and one radius

2. Using the degrees you got from the previous steps use a protractor to measure the biggest section (in our case 144 degrees, for the pear)

3. Continue using your protractor to make the sections glossary:

- outiler: number in a set of data that is much greater or much smaller than other values in the set

- census: a survey in which you ask the whole population

- sample survey: a survey in which you ask a portion of the population

- inference: what you deduct from looking at a set of data or graph

- central tendancy: the number that best represents the middle (median, mode, mean) THE END :)

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# Math- data management

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