Step: 1

Median is the data value which is the middle one in the ordered data set.

Step: 2

The middle value of Chris′s score is 65. Median of Chris′s score is 65.

Step: 3

The middle value of Mark′s score is 85. Median of Mark′s score is 83.

Step: 4

On comparing, Chris has a lower median than Mark.

[Since 65 is lower than 83.]

Step: 5

The average of the numbers of a data set is called mean.
Mean = s u m o f t h e d a t a v a l u e s n u m b e r o f d a t a v a l u e s

Step: 6

Mean of Chris′s score is 7 8 + 6 8 + 7 5 + 6 5 + 8 0 + 8 5 + 7 0 7 = 74.4

Step: 7

Mean of Mark′s score is 6 9 + 7 2 + 8 0 + 8 3 + 7 8 + 8 0 + 7 5 7 = 76.7

Step: 8

On comparing, Chris has a lower mean than Mark.

[Since 74.4 is lower than 76.7.]

Step: 9

So, Chris has a lower mean than Mark.

Correct Answer is : Chris has a lower mean than Mark.

Step: 1

Arrange the data values of Data A in ascending order: 120, 121, 122, 124, 128, 130, 133

Step: 2

Arrange the data values of Data B in ascending order: 112, 119, 120, 125, 126, 127, 128

Step: 3

Median is the middle data value in an ordered data set.

Step: 4

The middle value of Data A is 124. Median of Data A = 124

Step: 5

The middle value of Data B is 125. Median of Data B = 125

Step: 6

On comparing, Data B has a greater median than Data A.

[Since 125 is greater than 124.]

Correct Answer is : Data B

Female Customers | 10 | 10 | 5 | 32 | 24 | 18 | 12 | 8 | 10 | 11 |

Male Customers | 21 | 22 | 15 | 14 | 9 | 10 | 13 | 12 | 14 | 10 |

Step: 1

The average of the numbers of a data set is called mean.

Mean =s u m o f t h e d a t a v a l u e s n u m b e r o f d a t a v a l u e s

Mean =

Step: 2

Mean of the number calls made daily by female customers = 1 0 + 1 0 + 5 + 3 2 + 2 4 + 1 8 + 1 2 + 8 + 1 0 + 1 1 1 0 = 1 4 0 1 0 = 1 4

[Substitute the values and simplify]

Step: 3

Mean of the number calls made daily by male customers = 2 1 + 2 2 + 1 5 + 1 4 + 9 + 1 0 + 1 3 + 1 2 + 1 4 + 1 0 1 0 = 1 4 0 1 0 = 1 4

[Substitute the values and simplify]

Step: 4

On comparing, the mean of the number of calls made daily by female customers is equal to the mean of the number of calls made daily by male customers.

Correct Answer is : The mean of Female customers data is equal to that of Male customers data.

Data P | 6.3 | 6.1 | 6.7 | 6.6 | 6.8 | 6.4 |

Data Q | 6.3 | 6.8 | 6.8 | 6.3 | 6.7 | 6.1 |

Step: 1

Arrange the data values of Data P in ascending order: 6.1, 6.3, 6.4, 6.6, 6.7, 6.8

Step: 2

Arrange the data values of Data Q in ascending order: 6.1, 6.3, 6.3, 6.7, 6.8, 6.8

Step: 3

Median is the middle data value in an ordered data set.

Step: 4

Here we have two middle values. When there are two middle values, then Median = s u m o f t h e t w o m i d d l e v a l u e s 2

Step: 5

The two middle values of Data P are 6.4 and 6.6.
Median of Data P = 6 . 4 + 6 . 6 2 = 1 3 2 = 6 . 5

Step: 6

The two middle values of Data Q are 6.3 and 6.7.
Median of Data Q = 6 . 3 + 6 . 7 2 = 1 3 2 = 6 . 5

Step: 7

On comparing, both Data P and Data Q have equal median.

Correct Answer is : Both Data P and Data Q have equal median.

Data P | 2.4 | 3.1 | 2.7 | 3.6 | 1.4 | 2.8 |

Data Q | 3.8 | 2.5 | 1.8 | 1.3 | 2.4 | 2.1 |

Step: 1

The difference of Upper Quartile and Lower Quartile gives the value of interquartile range.

Step: 2

Arrange the data values of Data P in ascending order and find the lower quartile, upper quartile and interquartile range.

1.4, 2.4, 2.7, 2.8, 3.1, 3.6.

Lower Quartile = Median of lower half of the data = 2.4

Upper Quartile = Median of upper half of the data = 3.1

Interquartile Range = Upper Quartile - Lower Quartile = 3.1 - 2.4 = 0.7

1.4, 2.4, 2.7, 2.8, 3.1, 3.6.

Lower Quartile = Median of lower half of the data = 2.4

Upper Quartile = Median of upper half of the data = 3.1

Interquartile Range = Upper Quartile - Lower Quartile = 3.1 - 2.4 = 0.7

Step: 3

Arrange the data values of Data Q in ascending order and find the lower quartile, upper quartile and interquartile range.

1.3, 1.8, 2.1, 2.4, 2.5, 3.8.

Lower Quartile = Median of lower half of the data = 1.8

Upper Quartile = Median of upper half of the data = 2.5

Interquartile Range = Upper Quartile - Lower Quartile = 2.5 - 1.8 = 0.7

1.3, 1.8, 2.1, 2.4, 2.5, 3.8.

Lower Quartile = Median of lower half of the data = 1.8

Upper Quartile = Median of upper half of the data = 2.5

Interquartile Range = Upper Quartile - Lower Quartile = 2.5 - 1.8 = 0.7

Step: 4

Therefore, Data P and Data Q have equal interquartile range.

Correct Answer is : Both Data P and Data Q have equal interquartile range

M | 12 | 18 | 13 | 21 | 17 | 16 | 24 | 15 |

N | 17 | 11 | 24 | 27 | 15 | 23 | 20 | 13 |

Step: 1

The difference of Upper Quartile and Lower Quartile gives the value of interquartile range.

Step: 2

Arrange the data values of Data M in ascending order and find the lower quartile, upper quartile and interquartile range.

12, 13, 15, 16, 17, 18, 21, 24.

Lower Quartile = Median of lower half of the data =1 3 + 1 5 2 = 1 4

Upper Quartile = Median of upper half of the data =1 8 + 2 1 2 = 1 9 . 5

Interquartile Range = Upper Quartile - Lower Quartile = 19.5 - 14 = 5.5

12, 13, 15, 16, 17, 18, 21, 24.

Lower Quartile = Median of lower half of the data =

Upper Quartile = Median of upper half of the data =

Interquartile Range = Upper Quartile - Lower Quartile = 19.5 - 14 = 5.5

Step: 3

Arrange the data values of Data B in ascending order and find the lower quartile, upper quartile and interquartile range.

11, 13, 15, 17, 20, 23, 24, 27.

Lower Quartile = Median of lower half of the data =1 3 + 1 5 2 = 1 4

Upper Quartile = Median of upper half of the data =2 3 + 2 4 2 = 2 3 . 5

Interquartile Range = Upper Quartile - Lower Quartile = 23.5 - 14 = 9.5

11, 13, 15, 17, 20, 23, 24, 27.

Lower Quartile = Median of lower half of the data =

Upper Quartile = Median of upper half of the data =

Interquartile Range = Upper Quartile - Lower Quartile = 23.5 - 14 = 9.5

Step: 4

Therefore, Data M has lesser interquartile range than Data N.

[Since 5.5 is lesser than 9.5]

Correct Answer is : Data M has lesser interquartile range than Data N.

Step: 1

Mean = s u m o f t h e d a t a v a l u e s n u m b e r o f d a t a v a l u e s

[Formula.]

Step: 2

Mean of the given data of Rob's score = 5 + 6 + 6 + 7 4 = 2 4 4 = 6

[Substitute and simplify.]

Step: 3

Mean of the given data of Andy's score = 4 + 6 + 6 + 8 4 = 2 4 4 = 6

[Substitute and simplify.]

Step: 4

On comparing, both have an equal mean number of goals.

Correct Answer is : Both have an equal mean number of goals

Step: 1

Arrange the data values of Country 1 in ascending order: 1.89%, 2.9%, 5%, 6.83%, 9.01%, 12.91%, 13%, 14.56%.

Step: 2

Arrange the data values of Country 2 in ascending order: 0.09%, 1.02%, 2.9%, 2.9%, 4.86%, 11.23%, 12.91%, 13.02%.

Step: 3

Median is the middle data value in an ordered data set.

Step: 4

Here we have two middle values. When there are two middle values, then Median = s u m o f t h e t w o m i d d l e v a l u e 2

Step: 5

The two middle values of Country 1 are 6.83 and 9.01.
Median percentage of Country 1 = ( 6 . 8 3 + 9 . 0 1 ) 2 = 7.92%.

Step: 6

The two middle values of Country 2 are 2.9 and 4.86.
Median percentage of Country 2 = ( 2 . 9 + 4 . 8 6 ) 2 = 3.88%

Step: 7

On comparing, Country 1 has a greater median than Country 2.

Step: 8

The average of the numbers of a data set is called mean.
Mean = s u m o f t h e d a t a v a l u e s n u m b e r o f d a t a v a l u e s

Step: 9

Mean percentage of children suffering from vascular diseases in Country 1

=( 5 + 6 . 8 3 + 2 . 9 + 1 4 . 5 6 + 9 . 0 1 + 1 . 8 9 + 1 2 . 9 1 + 1 3 ) 8

=

Step: 10

Step: 11

= 8.263%

Step: 12

Mean percentage of children suffering from vascular diseases in Country 2

=( 2 . 9 + 1 . 0 2 + 1 2 . 9 1 + 1 3 . 0 2 + 4 . 8 6 + 2 . 9 + 0 . 0 9 + 1 1 . 2 3 ) 8

=

Step: 13

= 4 8 . 9 3 8

Step: 14

= 6.116%

Step: 15

On comparing, Country 1 has greater mean percentage than Country 2.

[Since 8.263 is greater than 6.116.]

Step: 16

So, Country 1 has greater mean percentage than country 2.

Correct Answer is : Country 1 has greater mean than Country 2

Company A | 4 | 5 | 5 | 5 | 5 | 6 | 7 | 6 | 4 | 5 |

Company B | 5 | 5 | 8 | 8 | 8 | 10 | 6 | 5 | 8 | 7 |

Step: 1

Mean =

Step: 2

Mean hourly pay for Company A = ( 4 + 5 + 5 + 5 + 5 + 6 + 7 + 6 + 4 + 5 ) 1 0 = 5 2 1 0 = $ 5 . 2

[Substitute the values and simplify]

Step: 3

Mean hourly pay for Company B = ( 5 + 5 + 8 + 8 + 8 + 1 0 + 6 + 5 + 8 + 7 ) 1 0 = 7 0 1 0 = $ 7

[Substitute the values and simplify]

Step: 4

On comparing, Company B has higher mean hourly pay than Company A. So, Phillips would join the Company B.

Correct Answer is : Company B

Edward | 90 | 70 | 50 | 45 | 65 |

Richard | 85 | 40 | 60 | 75 | 80 |

Step: 1

To find the standard deviation first we need to find the mean of the data.

Mean =s u m o f t h e d a t a v a l u e s n u m b e r o f d a t a v a l u e s

Mean =

Step: 2

Mean (X) of stamps of different countries collected by Edward = ( 9 0 + 7 0 + 5 0 + 4 5 + 6 5 ) 5 = 3 2 0 5 = 6 4

Step: 3

Mean (Y) of stamps of different countries collected by Richard = ( 8 5 + 4 0 + 6 0 + 7 5 + 8 0 ) 5 = 3 4 0 5 = 6 8

Step: 4

Standard deviation = ( x 1 - X ) 2 + ( x 2 - X ) 2 + . . . + ( x n - X ) 2 n

[X = mean of the data, x _{1}, x _{2}, x _{n} represents the data values.]

Step: 5

Standard deviation of stamps collected by Edward = ( x 1 - X ) 2 + ( x 2 - X ) 2 + ( x 3 - X ) 2 + ( x 4 - X ) 2 + ( x 5 - X ) 2 n

=( 9 0 - 6 4 ) 2 + ( 7 0 - 6 4 ) 2 + ( 5 0 - 6 4 ) 2 + ( 4 5 - 6 4 ) 2 + ( 6 5 - 6 4 ) 2 5

=6 7 6 + 3 6 + 1 9 6 + 3 6 1 + 1 5

=1 2 7 0 5

=2 5 4

= 15.94

=

=

=

=

= 15.94

Step: 6

Standard deviation of stamps collected by Richard = ( y 1 - Y ) 2 + ( y 2 - Y ) 2 + ( y 3 - Y ) 2 + ( y 4 - Y ) 2 + ( y 5 - Y ) 2 n

=( 8 5 - 6 8 ) 2 + ( 4 0 - 6 8 ) 2 + ( 6 0 - 6 8 ) 2 + ( 7 5 - 6 8 ) 2 + ( 8 0 - 6 8 ) 2 5

=2 8 9 + 7 8 4 + 6 4 + 4 9 + 1 4 4 5

=1 3 3 0 5

=2 6 6

= 16.31

=

=

=

=

= 16.31

Step: 7

On comparing, Richard has greater standard deviation than Edward.

Correct Answer is : Richard

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