1. 7. Displaying and interpreting single data sets
Study guide
7. Displaying and interpreting single data sets

2. Frequency tables
A frequency table lists the outcomes and how often (frequency) each outcome occurs.
Scores are listed in ascending order.
Tally column records the number of times the score occurred (groups of 5’s).
Frequency column is a count of each outcome.
HSC Hint – Add the numbers in the frequency column. It should equal the total number of scores.

3. Grouped frequency tables
Grouped frequency table organises the data into small groups or classes rather than as individual scores. Class centre is average of the boundaries and is used to calculate the mean.
HSC Hint – Class centres should increase by the same amount.

4. Cumulative frequency
Cumulative frequency is the frequency of the score plus the frequency of all the scores less than that score. It is the progressive total of the frequencies.
Score
Frequency
Cumulative Frequency 18 1 19 5 6 20 3 9 21 7 16
HSC Hint – The last number in the cumulative frequency column equals the total number of scores.

5. Range and interquartile range
Range = Highest score – Lowest score
Interquartile range is the difference between the first quartile and third quartile.
To calculate the interquartile range (IQR):
Arrange the data in increasing order.
Divide the data into two equal-sized groups. If n is odd, omit the median.
Find Q1 the median of the first group.
Find Q3 the median of the second group.
Calculate the interquartile range
HSC Hint – Interquartile range is not dependent on the extreme values like the range.

6. Frequency histogram
Frequency histogram is a column graph with equal intervals of the scores or class centres on the horizontal axis and the frequencies associated with these intervals shown by vertical rectangles.
HSC Hint – Score with the tallest rectangle is the mode.

7. Cumulative frequency histogram
Cumulative frequency histogram is a column graph with equal intervals of the scores or class centres on the horizontal axis and the cumulative frequencies associated with these intervals shown by vertical rectangles.
HSC Hint – Cumulative frequency histograms never decrease in height.

8. Frequency polygon
Frequency polygon is a line graph of a frequency table. It can be constructed by joining the mid-points of the histogram.  
HSC Hint – Range from a frequency polygon is calculated by using the horizontal axis (Highest − Lowest).

9. Cumulative frequency polygon
Cumulative frequency polygon or ogive is a line graph constructed by joining the top right hand corner of the rectangles in a cumulative frequency histogram. It is used to approximate the median.
HSC Hint – Cumulative frequency polygon is not constructed in the same way as a frequency polygon.

10. Box-and-whisker plot
A box-and-whisker plot is a graph that uses five-number summary – lower extreme, lower quartile, median, upper quartile and the higher extreme.
HSC Hint – To draw a box plot arrange the data in order before calculating the five-number summary.

11. Sector graph
Sector graph or pie chart presents data as sectors of a circle (‘slices’ of a ‘pie’). It shows the relationship or proportions of parts to a whole.
HSC Hint – Sector angle is calculated by multiplying the proportion of the whole by 360.

12. Divided bar graph
A divided bar graph shows the relationship or proportions of parts to a whole. It consists of bars or rectangles drawn to scale.
HSC Hint – Information from a divided bar graph is determined by measuring.

13. Radar charts
A radar chart looks like a spider web and is used to compare the performance of one or more entities.
HSC Hint – Line segments in a radar chart must be constructed accurately to ensure the information is valid.

14. Dot plot
A dot plot consists of a number line with each data point marked by a dot. When several data points have the same value, the points are stacked on top of each other.
HSC Hint – Dot plots are not suitable for large data sets.

15. Stem-and-leaf plot
A stem-and-leaf plot or stem plot is used to present a small (less than 50 values) numerical data set. The tens digit of the data values becomes the ‘stem’ and these are written in numerical order down the page. The ‘units’ digit becomes the ‘leaves’ and these are written in numerical order across the page.
HSC Hint – The numbers in the ‘leaves’ of a stem-and-leaf plot must be written in increasing order.