1. The Median of Grouped Data © Christine Crisp “Teach A Level Maths” Statistics 1

2. The Median of Grouped Data Finding the median of raw data is easy. e.g.1 Find the median of 3231172879233413 3432312823171397 The data must be put in numerical order: The median is the middle value, which we can see is the 5 th value, so, median = 23 The formula telling us which value we want is, where n is the number of data items. If n is an even number, we average the 2 middle values.

3. The Median of Grouped Data For an even number of items: The median is the middle value, which we can see is the 5½th value. i.e half way between the 5 th and 6 th value, so, e.g.1 Find the median of 3231172879233413 36 3432312823171397 The data must be put in numerical order: 36 The median is the value median =

4. The Median of Grouped Data e.g.2 Find the median of x12345 f47962 There are 28 observations so using we need: Accumulating the frequencies: 20114 Cu. f 54321x so, the 14th and 15th observations are both 3. The median is 3. We need to average the 14th and 15th numbers.

5. The Median of Grouped Data With a grouped distribution, we can only estimate the median. 36543Frequency, f 41 - 5031 - 4021 - 3011 - 201 - 10Length (cm) e.g. 3 There are 21 observations so we want to estimate the size of the 11 th one. It lies in the 3 rd class. Using a Cumulative Frequency Chart Using a Interpolation

6. The Median of Grouped Data 36543Frequency, f 41 - 5031 - 4021 - 3011 - 201 - 10Length (cm) e.g. 3 The first 2 classes have a cumulative frequency of 7, With a grouped distribution, we can only estimate the median. There are 21 observations so we want to estimate the size of the 11 th one. It lies in the 3 rd class.

7. The Median of Grouped Data 36543Frequency, f 41 - 5031 - 4021 - 3011 - 201 - 10Length (cm) e.g. 3 so to reach 11, we need 4 more. The first 2 classes have a cumulative frequency of 7, With a grouped distribution, we can only estimate the median. There are 21 observations so we want to estimate the size of the 11 th one. It lies in the 3 rd class.

8. The Median of Grouped Data 36543Frequency, f 41 - 5031 - 4021 - 3011 - 201 - 10Length (cm) e.g. 3 The first 2 classes have a cumulative frequency of 7, so to reach 11, we need 4 more. With a grouped distribution, we can only estimate the median. The 3 rd class has a frequency of 5 so we need to go part-way along this class. There are 21 observations so we want to estimate the size of the 11 th one. It lies in the 3 rd class.

9. The Median of Grouped Data 36543Frequency, f 41 - 5031 - 4021 - 3011 - 201 - 10Length (cm) e.g. 3 The first 2 classes have a cumulative frequency of 7, so to reach 11, we need 4 more. With a grouped distribution, we can only estimate the median. The 3 rd class has a frequency of 5 so we need to go part-way along this class. There are 21 observations so we want to estimate the size of the 11 th one. It lies in the 3 rd class.

10. The Median of Grouped Data 36543Frequency, f 41 - 5031 - 4021 - 3011 - 201 - 10Length (cm) e.g. 3 Coming up with our own method, needing 4 out of the frequency of 5, we would go 4/5 th along the class. The class is 10 wide The 3 rd class has a frequency of 5 so we need to go part-way along this class. The first 2 classes have a cumulative frequency of 7, so to reach 11, we need 4 more. With a grouped distribution, we can only estimate the median. There are 21 observations so we want to estimate the size of the 11 th one. It lies in the 3 rd class.

11. The Median of Grouped Data 36543Frequency, f 41 - 5031 - 4021 - 3011 - 201 - 10Length (cm) e.g. 3 Coming up with our own method, needing 4 out of the frequency of 5, we would go 4/5 th along the class. The class is 10 wideand 4 /5 th of 10 is 8. The first 2 classes have a cumulative frequency of 7, so to reach 11, we need 4 more. With a grouped distribution, we can only estimate the median. The 3 rd class has a frequency of 5 so we need to go part-way along this class. There are 21 observations so we want to estimate the size of the 11 th one. It lies in the 3 rd class.

12. The Median of Grouped Data 36543Frequency, f 41 - 5031 - 4021 - 3011 - 201 - 10Length (cm) e.g. 3 Coming up with our own method, needing 4 out of the frequency of 5, we would go 4/5 th along the class. The class is 10 wide We would go 8 along the class, which starts at 20·5, and 4 /5 th of 10 is 8. The first 2 classes have a cumulative frequency of 7, so to reach 11, we need 4 more. With a grouped distribution, we can only estimate the median. The 3 rd class has a frequency of 5 so we need to go part-way along this class. There are 21 observations so we want to estimate the size of the 11 th one. It lies in the 3 rd class.

13. The Median of Grouped Data 36543Frequency, f 41 - 5031 - 4021 - 3011 - 201 - 10Length (cm) e.g. 3 Coming up with our own method, needing 4 out of the frequency of 5, we would go 4/5 th along the class. The class is 10 wideand 4 /5 th of 10 is 8. We would go 8 along the class, which starts at 20·5, The first 2 classes have a cumulative frequency of 7, so to reach 11, we need 4 more. With a grouped distribution, we can only estimate the median. The 3 rd class has a frequency of 5 so we need to go part-way along this class. 20·5 There are 21 observations so we want to estimate the size of the 11 th one. It lies in the 3 rd class.

14. The Median of Grouped Data 36543Frequency, f 41 - 5031 - 4021 - 3011 - 201 - 10Length (cm) e.g. 3 Coming up with our own method, needing 4 out of the frequency of 5, we would go 4/5 th along the class. The class is 10 wide giving 28 ·5. and 4 /5 th of 10 is 8. We would go 8 along the class, which starts at 20·5, The first 2 classes have a cumulative frequency of 7, so to reach 11, we need 4 more. With a grouped distribution, we can only estimate the median. The 3 rd class has a frequency of 5 so we need to go part-way along this class. There are 21 observations so we want to estimate the size of the 11 th one. It lies in the 3 rd class.

15. The Median of Grouped Data We can use a cumulative frequency chart to estimate the median length upper class boundaryfrequency cumulative frequency 1 to 103 11 to 204 21 to 305 31 to 406 41 to 503 10.5 20.5 30.5 40.5 50.5 3 7 12 18 21

16. The Median of Grouped Data There are 21 observations so we want to estimate the size of the 11 th one. 11 28.5 So the median length = 28.5cm