Identify the mode of x and of y in the following table. x 4 5 6 7 8 f 1 5 5 6 4 y 4 3 2 1 0 f 27 28 29 27 25

Given that, the data is x 4 5 6 7 8 f 1 5 5 6 4 y 4 3 2 1 0 f 27 28 29 27 25 We know that, The mode is the value that appears most often in a set of data values. The value with highest frequency for x is 7 and the frequency is 6 The value with highest frequency for y is 2 and the frequency is 29 Thus the mode for x is 7 and the mode for y is 2 .

Find the modal class for x and for y in the following tables. x 0 - 4 - 14 - 20 f 5 9 8 y 3 - 6 7 - 11 12 - 20 f 66 80 134

Given that, the data is x 0 - 4 - 14 - 20 f 5 9 8 y 3 - 6 7 - 11 12 - 20 f 66 80 134 We know that, Frequency density of the modal class is f w where f is frequency and w is the width of the given class. Frequency density for x of the class 0 - 4 = 5 4 - 0 = 1 . 25 Frequency density for x of the class 4 - 14 = 9 14 - 4 = 0 . 9 Frequency density for x of the class 14 - 20 = 8 20 - 14 = 1 . 33 We know that, the modal class of the given data has the highest frequency density. Thus the modal class for x is 14 - 20 . Frequency density for y of the modal class 2 . 5 - 6 . 5 = 66 6 . 5 - 2 . 5 = 16 . 5 Frequency density for y of the modal class 6 . 5 - 11 . 5 = 80 11 . 5 - 6 . 5 = 16 Frequency density for y of the modal class 11 . 5 - 20 . 5 = 134 20 . 5 - 11 . 5 = 14 . 88 Thus the modal class for y is 16 . 5 .

EASY

AS and A Level

IMPORTANT

Earn 100

For $90$ values of $x$ and $64$ values of $y,$ it is given that $Σ (x - 1) = 72.9$ and $Σ (y + 1) = 201.6 .$ Find the mean value of all the values of $x$ and $y$ combined.

Important Questions on Measures of Central Tendency

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 2 - Measures of Central Tendency>EXERCISE 2A>Q 1

Find the mode(s) of the following sets of numbers : $12, 15, 11, 7, 4, 10, 32, 14, 6, 13, 19, 3$

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 2 - Measures of Central Tendency>EXERCISE 2A>Q 1

Find the mode(s) of the following sets of numbers: $19, 21, 23, 16, 35, 8, 21, 16, 13, 17, 12, 19, 14, 9$ .

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 2 - Measures of Central Tendency>EXERCISE 2A>Q 2

Which of the eleven words in this sentence is the mode?

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 2 - Measures of Central Tendency>EXERCISE 2A>Q 3

Identify the mode of $x$ and of $y$ in the following table.

$x$	$4$	$5$	$6$	$7$	$8$
$f$	$1$	$5$	$5$	$6$	$4$

$y$	$4$	$3$	$2$	$1$	$0$
$f$	$27$	$28$	$29$	$27$	$25$

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 2 - Measures of Central Tendency>EXERCISE 2A>Q 4

Find the modal class for $x$ and for $y$ in the following tables.

$x$	$0 -$	$4 -$	$14 - 20$
$f$	$5$	$9$	$8$

$y$	$3 - 6$	$7 - 11$	$12 - 20$
$f$	$66$	$80$	$134$

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 2 - Measures of Central Tendency>EXERCISE 2A>Q 5

A small company sells plass, which it cuts to size to lit into window frames. How could the company benefit from knowing the modal size of glass its customers purchase?

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 2 - Measures of Central Tendency>EXERCISE 2A>Q 6

Four classes of continuous data are recorded as

1 - 7, 8 - 16, 17 - 20

and

21 - 25 .

The class

1 - 7

has a frequency of

84

and there is no modal class. Find the total frequency of the other three classes.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 2 - Measures of Central Tendency>EXERCISE 2A>Q 7

Data about the times, in seconds, taken to run $100$ metres by $n$ adults are given in the following table.

Time $(x s)$	$13.6 ⩽ x < 15.4$	$15.4 ⩽ x < 17.4$	$17.4 ⩽ x < 19.8$
No. adults $(f)$	$a$	$b$	$27$

By first investigating the possible values of $a$ and of $b,$ find the largest possible value of $n,$ given that the modal class contains the slowest runners.

For 90 values of x and 64 values of y, it is given that Σx-1=72.9 and Σy+1=201.6. Find the mean value of all the values of x and y combined.

Important Questions on Measures of Central Tendency

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For $90$ values of $x$ and $64$ values of $y,$ it is given that $Σ (x - 1) = 72.9$ and $Σ (y + 1) = 201.6 .$ Find the mean value of all the values of $x$ and $y$ combined.