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Percentiles and quartiles - class-X

Description: percentiles and quartiles
Number of Questions: 15
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Tags: business economics and quantitative methods basic statistics for economics arithmetic mean maths measures of dispersion and skewness mode measures of dispersion averages and measures of spread median statistics and probability economics
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If the 2nd term of a GM series is 25, the first and 3rd terms will be _____.

median percentiles and quartiles range and mean deviation mode

  1. 5,125

  2. 105,5

  3. 5,105

  4. 25,125

Show answer
Correct Option: A
Explanation:

Geometric mean between two numbers is the mean proportion of the series. 

Therefore, let the two numbers be a and b 
a/25 = 25/b 

=>ab= 25 x 25

Also , a/b = 1/25

 b = 25a

so, a (25a) = 25 x 25

=>a2 = 25

=> a = 5

Now, b = 25(5)

        b = 125  

Therefore, the first and the 3rd terms are 5 and 125 respectively. 

_______ is used when most frequent occurring value if required. (discrete variable).

median percentiles and quartiles range and mean deviation mode

  1. Mode

  2. Mean

  3. Median

  4. None of above

Show answer
Correct Option: A
Explanation:

Mode is the highest occurring figure in a series. It is the value in a series of observation that repeats maximum number of times and which represents the whole series as most of the values in the series revolves around this value. 

Extreme values have _______ effect on mode.

median percentiles and quartiles range and mean deviation mode

  1. a large

  2. a small

  3. no

  4. None of above

Show answer
Correct Option: C
Explanation:

Mode is the highest occurring figure in a series. It is the value in a series of observation that repeats maximum number of times and which represents the whole series as most of the values in the series revolves around this value. Therefore, it is a positional average and it is not affected by the extreme values of the series as it is value within the series that occurs highest number of times.

Which of the following is a "Positional Average"?

median percentiles and quartiles range and mean deviation mode

  1. Arithmetic Mean

  2. Geometric Mean

  3. Harmonic Mean

  4. Median

Show answer
Correct Option: D
Explanation:

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 median, the middle most value of the series is taken as the representative value. Therefore, median is a positional average. 

Which of the following sentence is/ are wrong is relation to 'Mode'?

median percentiles and quartiles range and mean deviation mode

  1. It can be determined for a distribution with open ends

  2. It is not based on all the observations

  3. It is affected by extreme observations

  4. All of above

Show answer
Correct Option: C
Explanation:
Mode is the highest occurring figure in a series. It is the value in a series of observation that repeats maximum number of times and which represents the whole series as most of the values in the series revolves around this value. Therefore, it is a positional average and it is not affected by the extreme values of the series as it is value within the series that occurs highest number of times. 

_______ is that value of the variant which repeats maximum number of times in a distribution and around which other observations are densely distributed.

median percentiles and quartiles range and mean deviation mode

  1. Mean

  2. Median

  3. Harmonic mean

  4. Mode

Show answer
Correct Option: D
Explanation:

Mode is the highest occurring figure in a series. It is the value in a series of observation that repeats maximum number of times and which represents the whole series as most of the values in the series revolves around this value.

Which of the following sentence is/ are wrong in relation to 'Mode'?

median percentiles and quartiles range and mean deviation mode

  1. It is not affected by extreme observations

  2. It can be determined even for a distribution

  3. It cannot be located graphically

  4. All of above

Show answer
Correct Option: C
Explanation:
Mode is the highest occurring figure in a series. It is the value in a series of observation that repeats maximum number of times and which represents the whole series as most of the values in the series revolves around this value. Mode can be allocated graphically through bar diagrams as mode will be the highest bar in a bar graph as it occurs the highest number of times. 

The object of statistical averages is to ___________.

median percentiles and quartiles range and mean deviation mode

  1. help in comparison

  2. help in delusion making

  3. help in collection of data

  4. Both a & b

Show answer
Correct Option: D
Explanation:

Average is a method which ascertain a certain value by the use of observations from the data that represents the whole set of the data. Average is a single figure that represent the whole series. Therefore, average helps in completing the data, make the data short simply in a number that helps in decision making and initiates comparison between different variables.

Find out the range for the following prices of shirts in a shop.

Rupees
150
250
100
500
175
450
300
280
median percentiles and quartiles range and mean deviation mode

  1. Rs. 400

  2. Rs. 500

  3. Rs. 350

  4. Rs. 100

Show answer
Correct Option: A
Explanation:

Range is defined as the difference between the highest(or largest ) and lowest(or smallest) observed value in a series. It is the most simple and commonly understandable measures of dispersion. Therefore, it is the most affected measures of dispersion by the extreme values of the series. 

Range = H - L 

In the given series, H= 500 and L= 100 

Range = 500-100 = 400.

Find out the coefficient of range for the following prices of shirts in a shop.

Rupees
150
250
100
500
175
450
300
280
median percentiles and quartiles range and mean deviation mode

  1. 1.25

  2. 0.666

  3. 0.333

  4. 0.30

Show answer
Correct Option: B
Explanation:

Range is defined as the difference between the highest(or largest ) and lowest(or smallest) observed value in a series. It is the most simple and commonly understandable measures of dispersion. Therefore, it is the most affected measures of dispersion by the extreme values of the series. 

Range = H - L 

In the given series, H= 500 and L= 100 

Range = 500-100 = 400.

Coefficient of range is found by dividing the range with the sum of highest and lowest value of the series. 

Coefficient of range (CR) = R/ (H+L) 

                                          =400 / (500+100) 

                                          = 400/ 600 = 0.666

Calculation of Decile for individual data:
Find the $D _4$ and from the following data.
$20,22,24,26,28,30,32,34,36$

median percentiles and quartiles range and mean deviation mode

  1. 28

  2. 26

  3. 30

  4. 24

Show answer
Correct Option: B

Find $D _2$ for the following data:

Marks 10 20 30 40 50 60
No of Students 5 6 4 5 10 9
median percentiles and quartiles range and mean deviation mode

  1. 50 marks

  2. 20 marks

  3. 30 marks

  4. 40 marks

Show answer
Correct Option: B

Calculation of Decile for individual data:
Find the $D _8$ and from the following data.
$20,22,24,26,28,30,32,34,36$

median percentiles and quartiles range and mean deviation mode

  1. $D _8$=34

  2. $D _8$=32

  3. $D _8$=36

  4. $D _8$=28

Show answer
Correct Option: A

Find $D _4$ for the following data.

Marks 0-10 10-20 20-30 30-40 40-50 50-60
No of Students 5 6 5 5 10 9
median percentiles and quartiles range and mean deviation mode

  1. $D _4=30$

  2. $D _4=20$

  3. $D _4=40$

  4. $D _4=10$

Show answer
Correct Option: A

For the following grouped frequency distribution find the mode:

Class: 3-6 6-9 9-12 12-15 15-18 18-21 21-24
Frequency: 2 5 10 23 21 12 3
median percentiles and quartiles range and mean deviation mode

  1. 13.9

  2. 14.7

  3. 15.1

  4. 14.6

Show answer
Correct Option: A
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