Statistical Data Handling

Question 1

frequency definition

Answer 1

number of students who have chosen that category of fruit

if 100 students chose ‘Apple’ as their favourite fruit, so the frequency for the category ‘Apple’ is 100.

Question 2

total frequency definition

Answer 2

total number of students across all the categories

Question 3

statistical diagram name

Answer 3

frequency table

Question 4

frequency table 2 advantages

Answer 4

-used primarily to organise data collected
-easy to read the exact frequency for each category

Question 5

frequency table 2 disadvantages

Answer 5

-display of data not as visual and appealing as statistical graphs
-harder to compare frequencies across different categories than some statistical graphs

Question 6

statistical diagram name

Answer 6

pictogram

Question 8

advantage of pictogram

Answer 8

colourful and appealing

Question 9

3 disadvantages of pictogram

Answer 9

-it is difficult to draw the pictures, unless one uses a software
-it is difficult to draw a fraction of a picture, which may also result in misinterpretation
-the actual frequency in each category may be distorted and misinterpreted due to the different sizes of the pictures in different categories

Question 10

what kind of statistical diagram is this

Answer 10

bar graph

Question 11

2 things to note about pictures of pictograms

Answer 11

-size of each picture should be the same
-the pictures should be equally spaced out.

Question 12

how is proportionality of pictograms determined

Answer 12

The size of a picture is directly proportional to the number of students it represents (or the frequency).

Question 13

key/legend for pictogram indicated for what

Answer 13

The key (or legend) indicates the number of items represented by each picture and the number of pictures represents the frequency of each category.

Question 14

3 advantages of bar graph

Answer 14

-Easier to draw than a pictogram
-Do not have to draw a fraction of a picture
-Not distorted by different sizes of pictures

Question 15

how is the frequency of each category represented

Answer 15

length of the bar

Question 16

4 things to note for bar graph

Answer 16

-The bars must be of the same width.
-A space is left between two consecutive bars to distinguish between the categories.
-The length of a bar in a bar graph is directly proportional to the frequency,
-frequency axis starts from 0

Question 17

advantage of pie chart

Answer 17

easier to compare relative size of each category with the whole

Question 18

3 disadvantages of bar graph

Answer 18

-Less colourful and appealing than a pictogram
-More abstract because frequency is represented by length of each bar
-If the frequency axis does not start from zero, the data may be distorted or misinterpreted.

Question 19

6 disadvantages of pie chart

Answer 19

-More abstract than pictogram because frequency is represented by sector area (or angle)
-Harder to construct than a bar chart
-Will look very cluttered if there are many categories (or sectors)
-Difficult to compare two sectors of about the same size
-Sizes of sectors may be distorted and misinterpreted in a three-dimensional pie chart
-Difficult to determine the frequency of each category, unless it is stated inside each sector

Question 20

Answer 20

Question 21

two types of line graphs

Answer 21

categorical and numerical data

Question 22

categorical data line graph (3 points)

Answer 22

-Categorical data represent characteristics and can be divided into groups, e.g. type of fruit and gender. We cannot compare which categorical data are larger or smaller.
-Most categorical data cannot be ordered. However, some categorical data such as agree, neutral’ and disagree can still be ordered.
-Pictograms, bar graphs and pie charts are used to display categorical data. They may be used to display what appear to be numerical data, e.g. months and years. In this case, these
‘numerical data’ are treated as ‘labels.

Question 23

numerical data line graph (3 points)

Answer 23

-Numerical data consist of numbers. We can compare which data values are larger or smaller. However, not all numbers are numerical data, e.g. bus numbers, which are used as labels?
-All numerical data can be ordered.
-Line graphs are used to display numerical data.

Question 24

line graph advantage

Answer 24

Used to observe the rising or falling trend of a set of numerical data over a period of time

Question 25

line graph 2 disadvantages

Answer 25

-Must not read in between the plotted points, unlike graphs of linear functions. -We have to be careful and observe if the vertical axis starts from zero or otherwise. If the vertical axis does not start from zero, the data may be distorted and misinterpreted (just like for bar graphs). However, for data with small fluctuations, the vertical axis starting at zero will prevent the observation of these minor changes.

Question 26

Answer 26