Measures of Central Tendency Test

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Measures of Central Tendency Test - 47

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Weekly Quiz Competition

Question 1

1 / -0

What is the value of median for the following data:

Marks	No. of Students
$$5 - 14$$	$$10$$
$$15 - 24$$	$$18$$
$$25 - 34$$	$$32$$
$$35 - 44$$	$$26$$
$$45 - 54$$	$$14$$
$$55 - 64$$	$$10$$

$$28$$

$$30$$

$$32.94$$

$$33.18$$

Solution

Marks	No. of Students
4.5 −14.5	10
14.5 −24.5	18
24.5 −34.5	32
34.5 −44.5	26
44.5−54.5	14
54.5−64.5	10

Median is the middle most value of a given series that represents the whole class of the series. For a group data,

Median = L + [{(n/2) – B}/G] × w where

L is the lower class boundary of the group containing the median
n is the total number of values
B is the cumulative frequency of the groups before the median group
G is the frequency of the median group
w is the group width

Since the median is the middle value, which in this case is the 55th one, which is in the 24.5 −34.5 group. Therefore , 24.5 −34.5 is the median group so

L = 24.5
n = 110
B = 10 +18 = 28
G = 32
w = 10

Median= 24.5 + [{(110/2) – 28}/32] × 10

= 24.5 + 8.44
= 32.94

Question 2
1 / -0

A measure of central tendency that attempts to describe a set of data by identifying the central position within the data is?

A
Mean

B
Mode

C
Median

D
All the above

Solution

Positional average refers to the average which are taken out through observation from the series where a particular value from the series is picked up which represents the whole series.
In mean, the average of the whole series of observation is taken. In median, the middle most value of the series is taken whereas in mode, the value which occurs the highest number of times is taken as the representative value.
Question 3
1 / -0

If the two observations are $$10$$ and $$0$$, their arithmetic mean is _______.

A
$$10$$

B
$$0$$

C
$$5$$

D
none of the above

Solution

Arithmetic mean refers to the average amount in a given group of data. In this measure of central tendency, all the data are added up and then divided by the number of figures in the data in order to ascertain the mean.
Therefore,
Arithmetic mean $$= \dfrac{(10+0)}{2}$$

$$= \dfrac{10}{2}$$

$$= 5$$
Question 4
1 / -0

Find median of the following data.
Age greater than (Years) No. of Persons
$$0$$ $$230$$
$$20$$ $$218$$
$$30$$ $$200$$
$$40$$ $$165$$
$$50$$ $$123$$
$$60$$ $$73$$
$$70$$ $$288$$

A
$$31.5$$

B
$$41.5$$

C
$$41.6$$

D
$$31.6$$
Question 5
1 / -0

A measure of central location which splits the data set into two equal groups is called the.

A
Mean

B
Mode

C
Median

D
Standard deviation

Solution

Median is the middle most value of a series. So it divides a series of observations into two equal parts where 50% of the observations are below the median value and other 50% are above the median value.
Question 6
1 / -0

What is a reasonable explanation for a data set of the test score of 75 students in which the mean score is 81 and the median is 68?

A
An extremely low score

B
A number of typical scores

C
Too many scores

D
Two extremely high scores
Question 7
1 / -0

The mean is_____________________.

A
the statistical or arithmetic average

B
the middlemost score

C
the most frequently occurring score

D
the best representation for every set of data

Solution

Mean refers to the average amount in a given group of data. There are many ways to calculate arithmetic mean like direct method where all the data are added up and then divided by the number of figures in the data in order to ascertain the mean class or assumed mean method and step deviation method, the data of the given class is reduced into smaller units which makes it easy to do calculation and ascertain the mean of the class.
i.e.
$$Arithmetic\ mean= \dfrac{Sum\ of\ given\ numbers}{Total\ numbers}$$
Question 8
1 / -0

Find the median of the given mentioned observation $$15, 20, 45, 30, 60, 36$$.

A
$$32$$

B
$$33$$

C
$$47.5$$

D
None of the above

Solution

Median is the middle most value of a series. So when the series has odd number of elements then median can be calculated easily but when the series has even number of elements then the series has two middle values, so median is calculated by taking out the average of both the value.

The series is first arranged into either ascending or descending order. The formula to calculate median = (N+1) /2 th term of the series where N is the number of observation in the series.
The given series is first arranged into ascending; 15,20,30,36,45,60.
N= 6
median= (6+1)/2 th term = 7/2 th term = 3.5 th term
= ( value of 3rd term + value of 4th term)/2

= (30+36) /2 = 66/2 =33
Question 9
1 / -0

Given the following data set, what is the value of median (2 4 3 6 1 8 9 2 5 7 ).

A
2

B
4.7

C
4.5

D
10

Solution

Median is the middle most value of a series. So when the series has odd number of elements then median can be calculated easily but when the series has even number of elements then the series has two middle values, so median is calculated by taking out the average of both the value.
The given series is first arranged into ascending; 1,2,2,3,4,5,6,7,8,9
N= 10

median= (10+1)/2 th term = 11/2 th term = 5.5 th term
= ( value of 5th term + value of 6th term)/2

= (4+5) /2 = 9/2 = 4.5
Question 10
1 / -0

For calculation of median through interpolation formulae $$"h"$$ in the formulae is?

A
Frequency of the median

B
Lower limit of the median class

C
Width of the median class

D
Median

Solution

Median is the middle most value of a given series that represents the whole class of the series. For a group data,
Median = L + [{(n/2) – B}/G] × h where
h is the width of the median class.

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Re-Attempt Weekly Quiz Competition

Age greater than (Years)	No. of Persons
$$0$$	$$230$$
$$20$$	$$218$$
$$30$$	$$200$$
$$40$$	$$165$$
$$50$$	$$123$$
$$60$$	$$73$$
$$70$$	$$288$$

Measures of Central Tendency Test - 47

Result

Measures of Central Tendency Test - 47

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Rank

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SHARING IS CARING

Question 1

$$28$$

$$30$$

$$32.94$$

$$33.18$$

Solution

Question 2

Mean

Mode

Median

All the above

Solution

Question 3

$$10$$

$$0$$

$$5$$

none of the above

Solution

Question 4

$$31.5$$

$$41.5$$

$$41.6$$

$$31.6$$

Question 5

Mean

Mode

Median

Standard deviation

Solution

Question 6

An extremely low score

A number of typical scores

Too many scores

Two extremely high scores

Question 7

the statistical or arithmetic average

the middlemost score

the most frequently occurring score

the best representation for every set of data

Solution

Question 8

$$32$$

$$33$$

$$47.5$$

None of the above

Solution

Question 9

2

4.7

4.5

10

Solution

Question 10

Frequency of the median

Lower limit of the median class

Width of the median class

Median

Solution

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