How do you draw a cumulative frequency graph? (Part 1)

**Given this set of data...**

Time, t | Frequency | Cumulative Frequency |

0< t ≤10 | 22 | 22 |

10< t ≤15 | 32 | 54 |

15< t ≤20 | 26 | 80 |

20< t ≤25 | 15 | 95 |

25< t ≤30 | 5 | 100 |

For cumulative frequency graphs, remember to plot your points at the

**TOP**of each class boundary,

**DO NOT use midpoints**.

*See Part 2 of this card for the actual graph*

How do I calculate the estimated mean of grouped data?

Given this set of data for the test marks of a class of students, find an estimate for the mean test score of the class.

To actually calculate the mean...

Total of (frequency * midpoint) column ÷ Total Frequency

765 ÷ 23 =

Mark (m) | Number of students | Midpoint | Freq x midpoint |

0<m≤25 | 4 | 12.5 | 4x12.5=50 |

25<m≤35 | 5 | 30 | 5x30=150 |

35<m≤40 | 8 | 37.5 | 8x37.5=300 |

40<m≤45 | 5 | 42.5 | 5x42.5=212.5 |

45<m≤60 | 1 | 52.5 | 1x52.5=52.5 |

Totals: | 23 | 765 |

To actually calculate the mean...

Total of (frequency * midpoint) column ÷ Total Frequency

765 ÷ 23 =

**33.3**(1 d.p.)**Always****check**your answer makes senseHow do I calculate mean from a frequency table?

A school recorded the number of days that Year 9 pupils were absent last week.

Calculate the mean number of days absent

Sum of (number of days x number of pupils) ÷ Number of pupils

100÷200=0.5

Calculate the mean number of days absent

Number of days | Number of pupils | No of days x No of pupils |

0 | 144 | 0x144=0 |

1 | 27 | 1x27=27 |

2 | 18 | 2x18=36 |

3 | 8 | 3x8=24 |

4 | 2 | 4x2=8 |

5 | 1 | 5x1=5 |

Total: | 200 | 100 |

**To find the mean...**Sum of (number of days x number of pupils) ÷ Number of pupils

100÷200=0.5

*Notice that no midpoints are needed as this is not grouped data.*

Key features of different graph types

**Histograms:**

No gaps between bars.

**Frequency Histograms:**

Equal bar widths.

Frequency as y-axis

**Frequency Density Histograms:**

Different bar widths.

Frequency Density as y-axis

**Cumulative Frequency graphs:**

Points plotted at top of class-boundaries.

Smooth curve through points.

**Frequency Polygons:**

Frequencies plotted at class mid-points.

Points joined with straight-lines.

Why is a 7-point moving average appropriate for the daily sales of a shop?

If you get a question, for example, asking why a 7-point moving average is appropriate, it's probably something to do with there being seven days in a week.

A 4-point moving average is often used for seasons (Autumn, Winter, Spring, Summer) because there are 4 of them.

is a different question to

For the second question, you must be specific as to why a

A 4-point moving average is often used for seasons (Autumn, Winter, Spring, Summer) because there are 4 of them.

**Make sure you're answering the question though.****Why do we use a moving average?**is a different question to

**Why is a 4-point moving average appropriate to this data?**For the second question, you must be specific as to why a

**four**point moving average is used.Flashcard set info:

Author: mrfoxton

Main topic: Mathematics

Topic: Handling Data

Published: 18.10.2009

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