9. Statistics

Question 1

Bar chart (properties)

Answer 1

• Length of each bar represents quantity in question
• Width of each bar is equal + holds no significance
• Bars can be joined together or separate

Question 2

Pie chart (properties)

Answer 2

• Information is displayed using sectors of a circle (angles)
• Angles of the sectors calculated as such…

(Quantity / Total quantity) * 360

Question 3

Stem and leaf diagram (properties)

Answer 3

• Tens digit used as ‘stem’
• Units digit used as ‘leaf’
• First make diagram with order appearing in list
• Then rewrite it to correct order (ascending numerically)
• Repeat digits that repeat

Question 4

Frequency polygon (properties)

Answer 4

• Drawn by joining the midpoints of the tops of the bars on a frequency chart (aka a bar chart)
• Creates a graphical representation
• Mainly used to compare data because it’s easy to overlay two lines

Question 5

Histograms (properties)

Answer 5

• The frequency of data is shown by the area of each bar
• (Resemble bar charts → but in bar charts frequency is shown by the height of the bars)
• In histograms the bars often have varying widths
• Since area of bar = frequency → height is adjusted to correspond with width of the bar

→ Vertical axis = frequency density not frequency.

Question 6

Frequency density (found in histograms)

Answer 6

Frequency density = Frequency per unit data

Frequency density = Frequency / class width (interval)

Question 7

Mean

Answer 7

Mean = average → Total sum/ Number of numbers

Question 8

Median

Answer 8

Median = Middle value → Arranging numbers in order and choosing the number in the ‘middle’. If there are two middle numbers, an average is taken of them.

Question 9

Mode

Answer 9

Mode = Number which occurs most often.

Question 10

Using frequency tables to calculate the mean…

Answer 10

Multiply the data by the frequency.
Add everything together
Then divide by the sum of frequencies

Question 11

Using frequency tables to calculate the median…

Answer 11

Data point in the ‘middle’ of the frequency

Question 12

Using frequency tables to calculate the mode…

Answer 12

Data point with the highest frequency

Question 13

Finding the mean of data groups….

Answer 13

Multiply median of data groups with the frequency to find the total data.

Then divide by the frequency.

Question 14

Range

Answer 14

Range - Measures the spread or dispersion of a set of data

Range = highest value-lowest value

Question 15

Interquartile range

Answer 15

25th percentile or lower quartile = ¼ of the way through a data set. Eg. 3rd value if there are 12 values.

75th percentile or upper quartile = ¼ of the way through a data set. Eg. 9th value if there are 12 values.

50th percentile = median

interquartile range = upper quartile - lower quartile

The larger the interquartile range = The bigger the spread of data

Question 16

Cumulative frequency

Answer 16

Total frequency up to a given point