Chapter 6: measures of central tendency

Question 1

The population arithmetic mean is denoted by

Answer 1

M

Question 2

The sample arithmetic mean is denoted by

Answer 2

X bar

Question 3

One of the two mathermatical property of the mean

this equation value ∑(Xi-c)² is minimum when

Answer 3

c is equal to x bar

Question 4

One of the two mathermatical property of the mean

∑(Xi-M) is equal to

Answer 4

0

Question 5

If we add or subtract c to each one of the original observations, then what happens to the mean

Answer 5

the mean will increase or decrease by the same constant

Question 6

If we divide or multiply all original observations to constant c, then what happens to the mean?

Answer 6

the mean of the new data set is equal to the product of old data and c

Question 7

This is used if the individual observed values vary in their degree of importance

Answer 7

weighted mean

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Question 8

A modification of the arithmetic mean. This is an apppropriate alternative to arithmetic mean whenever there are outliers

Answer 8

trimmed mean

When the question says, get the 5 percent trimmed mean of the data – You should delete the top and bottom 5 percent

Question 9

This divides the array into two equal parts

Answer 9

Median

Question 10

what is the formula for median

Answer 10

Odd, Md = X(n+1/2)

2

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Question 11

Interpretation for the median

Answer 11

At least half of the observations are less than or equal to the median and at the same time at least half of the observations are greater than or equal to the median

Question 12

What is the property of the median

Answer 12

Outliers do not affect the meadian

Question 13

This is the most observed value

Answer 13

Mode

Question 14

What is the property of the mode

Answer 14

• It does not always exist or it may not be unique
• Outliers do not affect the mode

Question 15

What is the data requirement for mean

Answer 15

Atleast interval scale

Question 16

What is the data requirement for median

Answer 16

At least ordinal scale

Question 17

What is the data requirement for mode

Answer 17

Only nominal scale

Question 18

What is the property of the mean

Answer 18

It utilizes all of the observed values in the collection

Question 19

How to approximate for the median from grouped data (formula)

Answer 19

Md = LCB(md) + C (times the equation below)

those parenthesis means subscript

f(md)

Question 20

How to approximate for the MEAN from grouped data (formula)

Answer 20

N

from i to k

Where,
Fi is the frequency
Xi is the class mark
N is total observations or summation of fi
k is equal to total number of classes

Question 21

How to approximate for the mode in grouped data

Answer 21

Mo = LCBmo + C ((fmo-f1)/(2fmo-f1-f2))

where,
f1 is the frquency of the class preeceding the modal class
fmo is the frquency of the modal class
f2 is the the frquency of the class following the modal class

Question 22

What is the property of the mode

Answer 22

It may not always exist

Question 23

What is the property of the median

Answer 23

Outliers in a data set do not affect the median