Victor and Noor are investigating the area of postage stamps. They design these data collection sheets. Victor Noor Area, A cm 2 Tally Area, A cm 2 Tally 0 < A ≤ 2 0 - 10 2 < A ≤ 4 20 - 30 4 < A ≤ 6 40 - 50 6 < A ≤ 8 60 - 70 8 < A ≤ 10 80 - 90 10 < A ≤ 12 Whose data collection sheet would be more suitable for recording the areas of stamps? Give reasons for your answer.

Given: Victor and Noor are investigating the area of postage stamps. They design these data collection sheets. Victor Noor Area, A cm 2 Tally Area, A cm 2 Tally 0 < A ≤ 2 0 - 10 2 < A ≤ 4 20 - 30 4 < A ≤ 6 40 - 50 6 < A ≤ 8 60 - 70 8 < A ≤ 10 80 - 90 10 < A ≤ 12 A data collection sheet can be used to collect and organise data. All intervals should have the same width. The data being collected are continuous so each class interval should be written with inequality symbols. Here, the two problems with Noor's data collection sheet are The class intervals do not have the same width. Some classes are missing. Class intervals are not written with inequality symbols. Correct representation is 0 ≤ x < 10 , 10 ≤ x < 20 , . . . So, Noor should refine her data collection sheet. Therefore, Victor's data collection sheet would be more suitable for recording the areas of stamps.

Kim is marking essays written by her students. The number of words in the essays written by her students is shown below. 495 511 483 502 500 496 532 498 496 499 503 521 487 518 526 508 514 503 Design a frequency table for recording this information. Use 481 - 490 as the first class interval.

Kim is marking essays written by her students. The number of words in the essays written by her students is shown below. 495 511 483 502 500 496 532 498 496 499 503 521 487 518 526 508 514 503 We have to design a frequency table for recording this information, using 481 - 490 as the first class interval. A frequency distribution is a list, table (i.e.: frequency table) that displays the frequency of various outcomes in a sample. Steps to design a frequency table, Identify the smallest and the largest values. Here the smallest value is 487 and the largest value is 532 . Choose the suitable class interval that cover the given data. They are usually chosen to have equal width. Thus, the design of a frequency table for given data is shown below. Number of words ( n ) Tally Frequency 481 ≤ n ≤ 490 491 ≤ n ≤ 500 501 ≤ n ≤ 510 511 ≤ n ≤ 520 521 ≤ n ≤ 530 531 ≤ n ≤ 540

Kim is marking essays written by her students. The number of words in the essays written by her students is shown below. 495 511 483 502 500 496 532 498 496 499 503 521 487 518 526 508 514 503 Complete your frequency table.

Kim is marking essays written by her students. The number of words in the essays written by her students is shown below. 495 511 483 502 500 496 532 498 496 499 503 521 487 518 526 508 514 503 We have to design and complete a frequency table for recording this information, using 481 - 490 as the first class interval. A frequency distribution is a list, table (i.e.: frequency table) that displays the frequency of various outcomes in a sample. Steps to design a frequency table, Identify the smallest and the largest values. Here the smallest value is 487 and the largest value is 532 . Choose the suitable class interval that cover the given data. They are usually chosen to have equal width. Thus, the completed frequency table for given data is shown below. Number of words ( n ) Tally Frequency 481 ≤ n ≤ 490 | | 2 491 ≤ n ≤ 500 | | | | | 6 501 ≤ n ≤ 510 | | | | 4 511 ≤ n ≤ 520 | | | 3 521 ≤ n ≤ 530 | | 2 531 ≤ n ≤ 540 | 1

Gina designs a data collection sheet to record the number of cars passing her house every minute She tests her data collection sheet by recording the number of cars for 15oneminute intervals Number of cars Tally Total Under 20 2130 3140 4150 Over 50 Explain why Gina should refine her data collection sheet

MEDIUM

Lower Secondary Stage 9

IMPORTANT

Cambridge Lower Secondary Maths Stage 9: Student's Book>Chapter 10 - Data Collection and Averages>Exercise 2>Q 6

Gina designs a data collection sheet to record the number of cars passing her house every minute. She tests her data collection sheet by recording the number of cars for $15$ one-minute intervals.

Number of cars	Tally	Total
Under $20$
$21 - 30$
$31 - 40$
$41 - 50$
Over $50$

Design a new data collection sheet that might be more suitable for Gina to use.

MEDIUM

Lower Secondary Stage 9

IMPORTANT

Cambridge Lower Secondary Maths Stage 9: Student's Book>Chapter 10 - Data Collection and Averages>Exercise 2>Q 7

Victor and Noor are investigating the area of postage stamps. They design these data collection sheets.

Victor		Noor
Area, $A ({cm}^{2})$	Tally	Area, $A ({cm}^{2})$	Tally
$0 < A \leq 2$		$0 - 10$
$2 < A \leq 4$		$20 - 30$
$4 < A \leq 6$		$40 - 50$
$6 < A \leq 8$		$60 - 70$
$8 < A \leq 10$		$80 - 90$
$10 < A \leq 12$

Whose data collection sheet would be more suitable for recording the areas of stamps? Give reasons for your answer.

MEDIUM

Lower Secondary Stage 9

IMPORTANT

Cambridge Lower Secondary Maths Stage 9: Student's Book>Chapter 10 - Data Collection and Averages>Exercise 2>Q 8

Polly wants to investigate the heights of children aged

11, 12

and

13

years. Design a data collection sheet that will allow her to collect data about gender, age and height. Include some class intervals for height.

MEDIUM

Lower Secondary Stage 9

IMPORTANT

Cambridge Lower Secondary Maths Stage 9: Student's Book>Chapter 10 - Data Collection and Averages>Discuss

Why do you think that it is not useful to group data into a frequency table with lots of class intervals?

MEDIUM

Lower Secondary Stage 9

IMPORTANT

Cambridge Lower Secondary Maths Stage 9: Student's Book>Chapter 10 - Data Collection and Averages>Exercise 3>Q 1

Kim is marking essays written by her students. The number of words in the essays written by her students is shown below.

$495$	$511$	$483$	$502$	$500$	$496$	$532$	$498$	$496$
$499$	$503$	$521$	$487$	$518$	$526$	$508$	$514$	$503$

Design a frequency table for recording this information. Use $481 - 490$ as the first class interval.

MEDIUM

Lower Secondary Stage 9

IMPORTANT

Cambridge Lower Secondary Maths Stage 9: Student's Book>Chapter 10 - Data Collection and Averages>Exercise 3>Q 1

Kim is marking essays written by her students. The number of words in the essays written by her students is shown below.

$495$	$511$	$483$	$502$	$500$	$496$	$532$	$498$	$496$
$499$	$503$	$521$	$487$	$518$	$526$	$508$	$514$	$503$

Complete your frequency table.

MEDIUM

Lower Secondary Stage 9

IMPORTANT

Cambridge Lower Secondary Maths Stage 9: Student's Book>Chapter 10 - Data Collection and Averages>Exercise 3>Q 2

Mason measures the length (in cm) of some leaves:

11.4 6.3 9.8 13.2 8.5 16.3 5.4 7.9 10.2 11.5 8.6 7.0 6.6 8.7 12.1 9.9 8.7 10.7 8.5 11.2 14.8 17.2 12.6 10.4 8.7

Mason first uses this frequency table to summarise his data.

Length, $L (cm)$	Tally	Frequency
$0 < L \leq 10$
$10 < L \leq 20$
$20 < L \leq 30$
$30 < L \leq 40$

Complete Mason's frequency table.

MEDIUM

Lower Secondary Stage 9

IMPORTANT

Cambridge Lower Secondary Maths Stage 9: Student's Book>Chapter 10 - Data Collection and Averages>Exercise 3>Q 2

Mason measures the length (in cm) of some leaves:

11.4 6.3 9.8 13.2 8.5 16.3 5.4 7.9 10.2 11.5 8.6 7.0 6.6 8.7 12.1 9.9 8.7 10.7 8.5 11.2 14.8 17.2 12.6 10.4 8.7

Mason first uses this frequency table to summarise his data.

Length, $L (cm)$	Tally	Frequency
$0 < L \leq 10$
$10 < L \leq 20$
$20 < L \leq 30$
$30 < L \leq 40$

Write down a problem with Mason's frequency table.

Important Questions on Data Collection and Averages

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