Data Analysis

Hong Kong

Stage 1 - Stage 3

Lesson

Area charts are similar to line charts in that they both display quantitative data that changes over time. However, while a line chart shows how one variable changes over time (e.g. a product's sales figures from a particular shop), an area chart is used to show changes in cumulated totals over time (e.g. total sales figures). The area between axes and lines are commonly emphasized with different colours or patterns.

Area charts usually compares a number of data sets. For example, the area chart below compares the total revenue for three products. The difference between the lines indicates the amount of revenue made by each product. For example, in the fourth month, Product B made $\$3000$$3000 ($\$9000-\$6000$$9000−$6000 ).

Watch out!

Don't just look at the $y$`y`-axis to find a value at a particular point in time. You need to calculate the difference between the upper and lower lines to find the value of the variable.

The revenues generated per $\$1000$$1000 in a company from their four major products are shown in the area chart below.

a) What was the average monthly revenue generated by product A? Give your answer to the nearest cent if necessary.

Think: We need to add up all the figures for product A, then divide the total by $6$6 (the number of months).

Do:

Average monthly revenue | $=$= | $\frac{50000+60000+80000+60000+40000+30000}{6}$50000+60000+80000+60000+40000+300006 |

$=$= | $\frac{320000}{6}$3200006 | |

$=$= | $\$53333.33$$53333.33 |

b) What was the average monthly revenue generated by product B? Give your answer to the nearest cent if necessary.

Think: Now we need to find the difference between the upper and lower lines for each month, before adding each monthly revenue and dividing by the number of months.

Do:

Average monthly revenue | $=$= | $\frac{\left(135000-50000\right)+\left(165000-60000\right)+\left(130000-80000\right)+\left(155000-60000\right)+\left(125000-40000\right)+\left(100000-30000\right)}{6}$(135000−50000)+(165000−60000)+(130000−80000)+(155000−60000)+(125000−40000)+(100000−30000)6 |

$=$= | $\frac{135000+165000+130000+155000+125000+100000-320000}{6}$135000+165000+130000+155000+125000+100000−3200006 | |

$=$= | $\frac{490000}{6}$4900006 | |

$=$= | $\$81666.67$$81666.67 |

c) What was the median monthly revenue generated by product A?

Think: If we order the monthly revenues from smallest to largest, the median will be the middle value. Note that for an even number of values, the median is the average of the middle two values.

Do:

Order the monthly revenues: $30000,40000,50000,60000,60000,80000$30000,40000,50000,60000,60000,80000

Since there are $6$6 values, we take the average of the middle two, $50000$50000 and $60000$60000.

Median monthly revenue | $=$= | $\frac{50000+60000}{2}$50000+600002 |

$=$= | $\frac{110000}{2}$1100002 | |

$=$= | $\$55000.00$$55000.00 |

d) What was the range of the monthly revenue generated by product D?

Think: The range is the difference between the highest monthly revenue and the lowest monthly revenue for product D.

Do:

Highest monthly revenue | $=$= | $\$50000.00$$50000.00 (at April) |

Lowest monthly revenue | $=$= | $\$35000.00$$35000.00 (at February) |

Range of the monthly revenue | $=$= | $50000-35000$50000−35000 |

$=$= | $\$15000.00$$15000.00 |

A radar chart is a graphical method of displaying multivariate data (e.g. different features of an item, time periods etc). These graphs look a bit like spider webs, with each variable represented by arms (called radii) starting from the same point and spread out in a circle.

A line is drawn connecting the data values for each radii so it looks like a star. This helps us identify the frequency of each observations and whether there are any outliers.

The annual sales per $1000$1000 units of two products are shown in the following radar chart.

a) How many units of Product B were sold in March?

Think: Where is the Product B's red dot for March on the graph?

Do: The red dot for March is on the $7$7, which means $7000$7000 units of Product B were sold in March.

b) How many units of Product A were sold in November?

Think: This is similar to part A, except this time we're going to look at the blue line.

Do: The blue line is on the $4$4, so $4000$4000 units of Product A were sold in November.

c) How many units of Product A were sold throughout the entire year?

Think: We need to find the total sales of Product A for each month.

Do: $\left(8+3+9+4+2+10+7+3+1+6+4+10\right)\times1000=67000$(8+3+9+4+2+10+7+3+1+6+4+10)×1000=67000 units.