Skip to content### 4.2 Presentation of data

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**Content-specific conceptual understandings**

**Presentation of data (discrete and continuous): frequency distributions (tables).**

Class intervals will be given as inequalities, without gaps.

**Histograms. Cumulative frequency; cumulative frequency graphs; use to find median, quartiles, percentiles, range and interquartile range (IQR).**

Frequency histograms with equal class intervals. Not required: Frequency density histograms.

**Production and understanding of box and whisker diagrams.**

Use of box and whisker diagrams to compare two distributions, using symmetry, median, interquartile range or range. Outliers should be indicated with a cross.

Determining whether the data may be normally distributed by consideration of the symmetry of the box and whiskers.

**Exercises**

**Presentation of Data**

- A student counted how many cars passed his house in one-minute intervals for 30 minutes. His results were:

23, 22, 22, 22, 24, 22, 21, 21, 23, 23, 27, 21, 21, 22, 23, 25, 27, 26, 23, 23, 22, 27, 26, 25, 28, 26, 22, 20, 21, 20.

Display this data in a frequency table.

Draw a bar chart for this data. - The ages of 200 members of a tennis club are:

20, 22, 23, 24, 25, 25, 25, 26, 26, 26, 26, 28, 28, 29, 29, 29, 30, 30, 30, 30, 30, 30, 30, 32, 32, 33, 33, 33, 34, 34, 34, 34, 34, 34, 34, 34, 35, 35, 35, 35, 36, 36, 36, 36, 36, 37, 37, 37, 38, 38, 38, 39, 39, 39, 40, 40, 40, 41, 41, 41, 42, 42, 42, 42, 42, 42, 42, 42, 43, 43, 43, 43, 43, 43, 44, 44, 44, 44, 44, 44, 45, 45, 45, 45, 45, 45, 45, 45, 46, 46, 46, 46, 46, 46, 46, 46, 47, 47, 47, 47, 47, 47, 47, 47, 47, 48, 48, 48, 48, 48, 48, 48, 48, 48, 49, 49, 49, 49, 49, 49, 49, 49, 50, 50, 50, 50, 50, 50, 51, 51, 51, 51, 51, 51, 51, 52, 52, 52, 52, 52, 53, 53, 53, 53, 53, 53, 53, 53, 53, 54, 54, 54, 54, 55, 55, 55, 55, 55, 56, 56, 56, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 58, 58, 58, 59,

59, 59, 60, 60, 60, 60, 60, 61, 61, 61, 62, 62, 62, 63, 63, 63, 63, 64, 64, 64, 64, 65, 65, 68, 69.

Draw a grouped frequency table and a histogram for the data.

**Graphical representation – Frequency polygon**

- The table shows the age distribution of mathematics teachers

who work at Caring High School.

a) Is the data discrete or continuous?

b) How many mathematics teachers work at Caring High School?

c) Use your GDC to help you draw a fully labeled histogram to represent this data. Here are the exam scores for a group of 24 students. The maximum possible mark was 90. - Here are the exam scores for a group of 24 students. The maximum possible mark was 90.

47, 54, 63, 77, 23, 15, 66, 32, 56, 83, 16, 49, 52, 67, 44, 9, 62, 46, 38, 58, 37, 25, 55, 46

Construct a frequency distribution table with mark intervals of 0–9, 10–19, and so on, and find cumulative frequencies for each mark interval.

**Box and whisker diagrams**

- The depths of snow at a ski resort are collected every year for 12 years on 31 January. All data is in centimetres.

30, 75, 125, 55, 60, 75, 65, 65, 45, 120, 70, 110.

Find the range, the median, the lower quartile, the upper quartile and the interquartile range of the data set. Also, show the data in a box and whisker plot.

2. Sophy’s test scores for the year 2020:

76, 79, 76, 74, 75, 71, 85, 82, 82, 79, 81

Find the range, the median, the lower quartile, the upper quartile and the interquartile range of the data set of scores and show the data in a box and whisker plot.