Measures of Central Tendency Test

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Measures of Central Tendency Test - 17

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Weekly Quiz Competition

Question 1
1 / -0

Find the first quartiles for the following data.
$8, 11, 20, 10, 2, 17, 15, 5, 16, 15, 25, 6, 5$

A
$2$

B
$6$

C
$8$

D
$5$

Solution

First arrange the data set in order.
$2, 5, 5, 6, 8, 10, 11, 15, 15, 16, 17, 20, 25$
Here the median is the middle number $= 11$
So, the first quartile is the median of the lower half of the data.
Therefore, the first quartile is $5$ .

Question 2

1 / -0

Find the weighted mean of marks obtained by a student in certain examination if he has secured

75,80,67,90

marks in English, Tamil, Mathematics, social Science respectively, having corresponding weights

3, 2, 2, 1.

$75.16$

$76.12$

$62.17$

$78.12$

Solution

Subject	Marks obtained	Weights $w_i$	$x_iw_i$
English	$75$	$3$	$225$
Tamil	$80$	$2$	$160$
Mathematics	$67$	$2$	$134$
Social science	$90$	$1$	$90$
		$\Sigma w_i=8$	$\Sigma x_iw_i=609$

Weighted Arithmetic mean $=$ $\displaystyle\dfrac {\Sigma x_iw_i}{\Sigma w_i}$ $=609/8$
Weighted Arithmetic mean $= 76.125$

Question 3

1 / -0

Marks	10-20	20-30	30-40	40-50	50-60
Frequency	4	10	20	40	50

The following frequency distribution shows the marks obtained by

124

students in Economy at a certain school. Find the arithmetic mean using the direct method.

$50$ marks

$80$ marks

$30$ marks

$45$ marks

Solution

Answer:- Direct Method:

Marks	Frequency	$x_i$	$f_i x_i$
$10-20$	$4$	$15$	$60$
$20-30$	$10$	$25$	$250$
$30-40$	$20$	$35$	$700$
$40-50$	$40$	$45$	$1800$
$50-60$	$50$	$55$	$2750$
	$\Sigma f_i = 124$		$\Sigma f_i x_i = 5560$

Mean = \cfrac{\Sigma f_i x_i}{\Sigma f_i}

= \cfrac{5560}{124} =44.83 \simeq 45marks.

Question 4
1 / -0

During the first period in the class, Elsa's math quiz scores were $90, 92, 93, 88, 95, 88, 97, 87$ and $98$ . What was the median quiz score?

A
$90$

B
$91$

C
$88$

D
$92$

Solution

The median of a set of data is the middlemost number in the set.
So, first arrange the data in order.
$87, 88, 88, 90, 92, 93, 95, 97, 98$
The median quiz score is $92$ .
Question 5
1 / -0

Find the mode of the following data
$58, 35, 54, 32, 54, 58, 34, 35, 35, 32, 58, 35, 35, 89, 58, 32, 32, 89.$

A
$35$

B
$58$

C
$32$

D
$89$

Solution

Given, $58, 35, 54, 32, 54, 58, 34, 35, 35, 32, 58, 35, 35, 89, 58, 32, 32, 89.$
The mode is the value which appears most often. In the above data the value which appears most often is $35$ , since it appears $5$ times. \
So, mode is $35$ .
Question 6
1 / -0

Choose the formula used for arithmetic mean of grouped data by Assumed mean method is

A
$\bar { x } = A - \dfrac { \sum { fd } }{ \sum { f } }$

B
$\bar { x } = A + \dfrac { \sum { fd } }{ \sum { f } }$

C
$\bar { x } = A \times \dfrac { \sum { fd } }{ \sum { f } }$

D
$\bar { x } = { A } / { \dfrac { \sum { fd } }{ \sum { f } } }$

Solution

The formula used for arithmetic mean of grouped data by shortcut method is $\bar { x } = A + \dfrac { \sum { fd } }{ \sum { f } }$
$A =$ Assumed mean of the given data
$\sum { f } =$ Summation of the frequencies given in the grouped data
$\sum { fd } =$ Summation of the frequencies and deviation of a given mean data
$d =$ deviation of a mean data
$\bar { x } =$ arithmetic mean
Question 7
1 / -0

Identify in which ideal measure of central tendency used to find the middle value, if the data are ordinal?

A
mean

B
median

C
mode

D
range

Solution

Median is the ideal measure of central tendency used to find the middle value, if the data are ordinal.
Example: Consider the data: $1, 2, 3, 4, 5, 5, 6, 3, 3, 2, 2, 1, 2$
First arrange the data in ordinal.
So, $1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 5, 5, 6$
So, $3$ is the median.
Median is the middle number.
Question 8
1 / -0

Which ideal measure of central tendency used to find the middle value, if the data are categorical?

A
mean

B
median

C
mode

D
range

Solution

Mode is the ideal measure of central tendency used to find the middle value, if the data are categorical.
Example: Discrete data: $1, 2, 3, 4, 5, 5, 6, 3, 3, 2, 2, 1, 2$
Mode is the most occurring value.
Here $2$ is the mode.
Question 9
1 / -0

The lower quartile is the value of the middle of the first set, where $25\%$ of the values are _____ than $Q_1$ and $75\%$ are larger.

A
longer

B
larger

C
smaller

D
higher

Solution

The lower quartile is the value of the middle of the first set, where $25\%$ of the values are smaller than $Q_1$ and $75\%$ are larger.
Example: $2, 5, 5, 6, 8, 10, 11$
Here the median is the middle number $= 6$
So, the first quartile is the median of the lower half of the data.
Then, the lower quartile of the first half will be $2, 5, 5$ which is $25\%$ of the given data
So, the remaining $75\%$ numbers can be considered as larger.
Question 10
1 / -0

The ______ is the median of of the lower half of the data set.

A
quartile

B
upper quartile

C
range

D
lower quartile

Solution

The lower quartile is the median of of the lower half of the data set.
Example: consider the data set: $10, 20, 30, 40, 50, 60, 70, 80, 90, 100$
The median of the lower half of the data set is $10, 20, 30, 40, 50$
So, the lower quartile $= 30$ .

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Re-Attempt Weekly Quiz Competition

Measures of Central Tendency Test - 17

Result

Measures of Central Tendency Test - 17

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SHARING IS CARING

Question 1

222

666

888

555

Solution

Question 2

75.1675.1675.16

76.1276.1276.12

62.1762.1762.17

78.1278.1278.12

Solution

Question 3

505050 marks

808080 marks

303030 marks

454545 marks

Solution

Question 4

909090

919191

888888

929292

Solution

Question 5

353535

585858

323232

898989

Solution

Question 6

xˉ=A−∑fd∑f\bar { x } = A - \dfrac { \sum { fd } }{ \sum { f } } xˉ=A−∑f∑fd​

xˉ=A+∑fd∑f\bar { x } = A + \dfrac { \sum { fd } }{ \sum { f } } xˉ=A+∑f∑fd​

xˉ=A×∑fd∑f\bar { x } = A \times \dfrac { \sum { fd } }{ \sum { f } } xˉ=A×∑f∑fd​

xˉ=A/∑fd∑f\bar { x } = { A } / { \dfrac { \sum { fd } }{ \sum { f } } }xˉ=A/∑f∑fd​

Solution

Question 7

mean

median

mode

range

Solution

Question 8

mean

median

mode

range

Solution

Question 9

longer

larger

smaller

higher

Solution

Question 10

quartile

upper quartile

range

lower quartile

Solution

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Question Analysis

My Perfomance

Score

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Rank

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Results Announcement on: coming Monday

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$2$

$6$

$8$

$5$

$75.16$

$76.12$

$62.17$

$78.12$

$50$ marks

$80$ marks

$30$ marks

$45$ marks

$90$

$91$

$88$

$92$

$35$

$58$

$32$

$89$

$\bar { x } = A - \dfrac { \sum { fd } }{ \sum { f } }$

$\bar { x } = A + \dfrac { \sum { fd } }{ \sum { f } }$

$\bar { x } = A \times \dfrac { \sum { fd } }{ \sum { f } }$

$\bar { x } = { A } / { \dfrac { \sum { fd } }{ \sum { f } } }$