The mean of 6 , 29 , 3 , 14 , q , q + 8 , q 2 and 10 - q is 20 . Find the possible values of q .

Given that, the mean of 6 , 29 , 3 , 14 , q , q + 8 , q 2 and ( 10 - q ) is 20 . We know that, mean = sum of all observations number of observations ⇒ q 2 + q + 70 8 = 20 ⇒ q 2 + q - 90 = 0 ⇒ ( q - 9 ) ( q + 10 ) = 0 , so q = 9 or q = - 10 Thus the possible values of q are 9 or - 10 .

EASY

AS and A Level

IMPORTANT

Earn 100

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.

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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 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.

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 8

Three classes of continuous data are given as

0 ⩽ x < 4, 4 ⩽ x < 10

and

10 ⩽ x < 18 .

The frequency densities of the classes

0 ⩽ x < 4

and

10 ⩽ x < 18

are in the ratio

4 : 3

and the total frequency of these two classes is

120 .

Find the least possible frequency of the modal class, given that the modal class is

4 ⩽ x < 10 .

EASY

AS and A Level

IMPORTANT

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

Calculate the mean of the following sets of numbers: $28, 16, 83, 72, 105, 55, 6$ and $35$

EASY

AS and A Level

IMPORTANT

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

Calculate the mean of the following sets of numbers:

$7.3, 8.6, 11.7, 9.1, 1.7$ and $4.2$

EASY

AS and A Level

IMPORTANT

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

Calculate the mean of the following sets of numbers:

$3 \frac{1}{2}, 5 \frac{1}{4}, 9 \frac{3}{4}, - 4 \frac{1}{4}$ and $7 \frac{3}{8} .$

EASY

AS and A Level

IMPORTANT

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

The mean of

15, 31, 47, 83, 97, 119

and

p^{2}

63 .

Find the positive value of

p .

EASY

AS and A Level

IMPORTANT

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

The mean of

6, 29, 3, 14, q, (q + 8), q^{2}

and

(10 - q)

20 .

Find the possible values of

q .

EASY

AS and A Level

IMPORTANT

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

Given that: $n = 14$ and $Σ x = 325.5,$ find $\bar{x}$

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.

Important Questions on Measures of Central Tendency

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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.