Cumulative Frequency – group task



LESSON 4 - Measuring Spread of Data

1) In Pairs - Read the following scenario and answer the question as best you can:

Suppose you have two types of biscuit packing machines in your factory, A and B. Each type of machine is supposed to insert 200g of biscuits into a packet. If packets are overweight or underweight you could be losing profits or running the risk of prosecution from the government trading standards office. In order to guide your future purchasing decisions, you decide to test which type of machine, A or B, is more reliable. As part of your testing procedure, you take a random sample of ten packets of biscuits from each machine and record the mass of each packet, to the nearest gram. Here are the results:

Machine A (mass in grams): 196, 198, 198, 199, 200, 200, 201, 201, 202, 205

Machine B (mass in grams): 195, 195, 195, 198, 200, 201, 203, 204, 204, 205

Which type of machine, A or B, is the best one to buy in the future? Explain your reasoning, showing any calculations you used to help you make your decision.

2) As with our Problem about choosing a basketball player for KT Sonicboom, we found that sometimes the measures of spread are not enough to get a clear picture of a set of data.

• Give examples of situations where it is important to measure the spread of a data set

• What methods do you already know for measuring the spread of a data set?

Which are the most sophisticated? Which are the most problematic and why?

• What was your conclusion to the question in the above scenario and why?

Cumulative Frequency – group task

Take 15 minutes to read and digest the following scenario and questions and discuss it with a partner.

Cumulative frequency graphs answer questions such as

“What proportion of the data has values less than …?”

With grouped data the first step is to produce a table of cumulative frequencies (the sum of the frequencies up to each particular class). These are then plotted against the corresponding upper class boundaries. These points are then connected by a smooth curve.

Cumulative frequency on the y-axis is plotted against the observed value on the x-axis.

Describe the shape the graph would take. WHY?

Scenario

In studying bird migration a standard technique is to put coloured rings around the legs of the young birds at their breeding colony. This means that the source of any bird (with a coloured ring) later seen somewhere else can be identified. The following data, which refer to the recoveries of razorbills, consist of the distances (measured in hundreds of miles) between the recovery point and the breeding colony. We can illustrate the data using a cumulative frequency curve and estimate the distance exceeded by 50% of the birds.

| |

|Distance (miles) x |Frequency |Cumulative Frequency |

|x < 100 |2 |2 |

|100 ( x < 200 |2 |4 |

|200 ( x < 300 |4 |8 |

|300 ( x < 400 |3 |11 |

|400 ( x < 500 |5 |16 |

|500 ( x < 600 |7 |23 |

|600 ( x < 700 |5 |28 |

|700 ( x < 800 |2 |30 |

|800 ( x < 900 |2 |32 |

|900 ( x < 1000 |0 |32 |

| 1000 ( x < 1500 |2 | 34 |

|1500 ( x < 2000 |0 |34 |

|2000 ( x < 2500 |2 |36 |

Textbook help MYP 5 PLUS page 191 Section F, example 6.

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Read and make notes on the information given on page 194 Sections G of your MYP 5 PLUS text example 7, 8, 9 as needed.

The graph below shows how the interquartile range is found and how quartiles are related to a Box Plot.

Use the graph to calculate an approximation for the interquartile range for your data.

Textbook help MYP 5 PLUS page 196 Section H, example 10 as needed.

Construct a Box and Whisker Plot below – Draw a suitable scale on the axis and show the 5 key values.

Practice

1. Below are two sets of data. For each set find the upper and lower quartiles (Q1 and Q3) and the median (Q2) and the interquartile range. For textbook help with this section, refer to page 286, and read examples 4, 5.

a) 3, 3, 3, 4, 4, 4, 5, 6 b) 2, 2, 3, 3, 3, 4, 4, 5, 6, 6, 7, 10

Draw the 2 box and whisker plots below.

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Write 2 observations when comparing both sets of data.

i.

ii.

2. Here is the time (in minutes) taken by two service providers to get a specific job completed.

[pic]

Interpretations:

a) What interpretation might you make of the long whisker on the left of Service B?

b) Explain what the different size boxes for each service mean when comparing the two providers?

c) Write 3 more interpretative statements comparing the two Service Providers.

d) Which provider would you choose? Explain your choice.

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The final value in the cumulative frequency column represents what?

What does the 28 represent?

The graph (when drawn accurately) tells us that 50% of the birds had travelled for more than 520 miles. To get this answer we look at 18 on the vertical scale and read a value off the horizontal scale. Why?

What is the RANGE of a set of data? What are the advantages/disadvantages with this measure?

What are Quartiles? How do we find them?

What is the Interquartile Range? What does it show you about a set of data?

What are the advantages/disadvantages with the interquartile range?

Box and Whisker Plot

This is another graphical representation using the 5 key data points in a distribution:

Maximum value, minimum value Q1, Q2 and Q3.

What does the box in the middle of the box and whisker plot represent about the data?

What do the whiskers at each end represent?

Show your work here

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