A hotel has 90 rooms. The table summarises information about the number of rooms occupied each day for a period of 200 days. Number of rooms occupied 1 - 20 21 - 40 41 - 50 51 - 60 61 - 70 71 - 90 Frequency 10 32 62 50 28 18 Draw a cumulative frequency graph on graph paper to illustrate this information.

Given Number of rooms occupied 1 - 20 21 - 40 41 - 50 51 - 60 61 - 70 71 - 90 Frequency 10 32 62 50 28 18 The cumulative frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors . Number of rooms occupied < 20 < 40 < 50 < 60 < 70 < 90 Cumulative Frequency 10 42 104 154 182 200 On Y-axis take draw cumulative frequency and on X-axis as number of rooms occupied

A hotel has 90 rooms. The table summarises information about the number of rooms occupied each day for a period of 200 days. Number of rooms occupied 1 - 20 21 - 40 41 - 50 51 - 60 61 - 70 71 - 90 Frequency 10 32 62 50 28 18 Draw a cumulative frequency graph on graph paper to illustrate this information. Estimate the number of days when more than 30 rooms were occupied.

Given Number of rooms occupied 1 - 20 21 - 40 41 - 50 51 - 60 61 - 70 71 - 90 Frequency 10 32 62 50 28 18 The cumulative frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors . Number of rooms occupied < 20 < 40 < 50 < 60 < 70 < 90 Cumulative Frequency 10 42 104 154 182 200 On Y-axis take draw cumulative frequency and on X-axis as number of rooms occupied Number of days more than thirty rooms were occupied = 200 - (cf-value at 30 . 5 rooms) = 200 - ( 20 to 26 ) = 174 to 180 days

A hotel has 90 rooms. The table summarises information about the number of rooms occupied each day for a period of 200 days. Number of rooms occupied 1 - 20 21 - 40 41 - 50 51 - 60 61 - 70 71 - 90 Frequency 10 32 62 50 28 18 Draw a cumulative frequency graph on graph paper to illustrate this information. On 75 % of the days at most n rooms were occupied. Estimate the value of n .

Given Number of rooms occupied 1 - 20 21 - 40 41 - 50 51 - 60 61 - 70 71 - 90 Frequency 10 32 62 50 28 18 The cumulative frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors . Number of rooms occupied < 20 < 40 < 50 < 60 < 70 < 90 Cumulative Frequency 10 42 104 154 182 200 On Y-axis take draw cumulative frequency and on X-axis as number of rooms occupied 75 % of 200 = 150 Number of rooms at (cf-value of ) 150 is 58 , 59 or 60 .

EASY

AS and A Level

IMPORTANT

Earn 100

A histogram is drawn with three columns whose widths are in the ratio $1 : 2 : 4$ . The frequency densities of these classes are in the ratio $16 : 12 : 3$ , respectively.

Given that the total frequency of the data is $390$ , find the frequency of each class.
The classes with the two highest frequencies are to be merged and a new histogram drawn. Given that the height of the column representing the merged classes is to be $30 cm$ , find the correct height for the remaining column.

Important Questions on Representation of Data

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 1 - Representation of Data>END-OF-CHAPTER REVIEW EXERCISE 1>Q 7

A histogram is drawn with three columns whose widths are in the ratio $1 : 2 : 4$ . The frequency densities of these classes are in the ratio $16 : 12 : 3$ , respectively.

Given that the total frequency of the data is $390$ , find the frequency of each class.

The classes with the two highest frequencies are to be merged and a new histogram drawn. Given that the height of the column representing the merged classes is to be

30 cm

, find the correct height for the remaining column.

Explain what problems you would encounter if asked to construct a histogram in which the classes with the two lowest frequencies are to be merged.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 1 - Representation of Data>END-OF-CHAPTER REVIEW EXERCISE 1>Q 8

The histograms below illustrate the number of hours of sunshine during August in two regions, $A$ and $B$ . Neither region had more than $8$ hours of sunshine per day.

Question Image

Explain how you know that some information for one of the regions has been omitted.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 1 - Representation of Data>END-OF-CHAPTER REVIEW EXERCISE 1>Q 8

The histograms below illustrate the number of hours of sunshine during August in two regions, $A$ and $B$. Neither region had more than 8 hours of sunshine per day.

Question Image

After studying the histograms, two students make the following statements.

- Bindu: There was more sunshine in region A than in region $B$ during the first $2$ weeks of August.
- Janet: In August there was less sunshine in region $A$ than in region $B$ .
Discuss these statements and decide whether or not you agree with each of them.In each case, explain your reasoning.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 1 - Representation of Data>END-OF-CHAPTER REVIEW EXERCISE 1>Q 9

A hotel has $90$ rooms. The table summarises information about the number of rooms occupied each day for a period of $200$ days.

Number of rooms occupied	$1 - 20$	$21 - 40$	$41 - 50$	$51 - 60$	$61 - 70$	$71 - 90$
Frequency	$10$	$32$	$62$	$50$	$28$	$18$

Draw a cumulative frequency graph on graph paper to illustrate this information.

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 1 - Representation of Data>END-OF-CHAPTER REVIEW EXERCISE 1>Q 9

A hotel has $90$ rooms. The table summarises information about the number of rooms occupied each day for a period of $200$ days.

Number of rooms occupied	$1 - 20$	$21 - 40$	$41 - 50$	$51 - 60$	$61 - 70$	$71 - 90$
Frequency	$10$	$32$	$62$	$50$	$28$	$18$

Draw a cumulative frequency graph on graph paper to illustrate this information.

Estimate the number of days when more than $30$ rooms were occupied.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 1 - Representation of Data>END-OF-CHAPTER REVIEW EXERCISE 1>Q 9

A hotel has $90$ rooms. The table summarises information about the number of rooms occupied each day for a period of $200$ days.

Number of rooms occupied	$1 - 20$	$21 - 40$	$41 - 50$	$51 - 60$	$61 - 70$	$71 - 90$
Frequency	$10$	$32$	$62$	$50$	$28$	$18$

Draw a cumulative frequency graph on graph paper to illustrate this information.

On $75 %$ of the days at most $n$ rooms were occupied. Estimate the value of $n$ .

Important Questions on Representation of Data

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