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# Graphs and Charts 2

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## Graphs and Charts 2

**Key Points**

**1.** Cumulative Frequency simply means adding the frequencies up as you go along.

**2.** When plotting the graph, always plot points using the **upper value **of each group.

**3.** Cumulative frequency is always plotted on the vertical axis (up the side) and the range of data goes across the bottom.

**4.** The shape of a cumulative frequency curve looks like a 'stretched S' and is called an **ogive.**

**5.** The more "stretched-out" the 'S' the more spread out is the data. An 'S' with a very steep middle section indicates the data being tightly grouped around the median. **(See diagram below):**

**Black line** = Very tight distribution grouped around the median.

**Red line** = Much more widely spread distribution. Large interquartile range.

A Cumulative Frequency graph is used to provide estimates of the **median** (and **quartiles**) when the data is **grouped.**
(Remember that with grouped data you cannot say what the Median is, only which group it is in!)

**We can get 4 main pieces of information from a Cumulative Frequency graph:**

**1. Median** - go halfway up the cumulative frequency axis, read across and down then read the median from the **bottom scale.**

**2. Lower Quartile** - go a quarter of the way up the cumulative frequency axis, read across and down then read the Lower Quartile from the **bottom scale.**

**3. Upper Quartile **- go three-quarters of the way up the cumulative frequency axis, read across and down then read the Upper Quartile from the **bottom scale.**

**4. Inter-Quartile Range** - the difference between the Lower Quartile and the Upper Quartile.

**An example**

A zookeeper measures the lengths of all the snakes in a zoo and records the results in a table:

He then constructs the following Cumulative Frequency graph and reads the Median, Lower and Upper Quartiles and finds the Inter-Quartile Range.

See if you can construct a Cumulative Frequency graph in the same way using the table below which shows the weights of pupils in a year-group.

**Type in the Cumulative Frequency in the dark blues boxes and click Mark Answer to see if your are correct:**