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Measures of Central Tendency

Question
ICSEENIMA10018838

The mean of following numbers is 68. Find the value of  ‘x’.  45,  52,  60,  x,  69,  70,  26,  81  and  94  Hence estimate the median. 

Solution

Mean = Sum of all observationsTotal number of observations 68 = 45 + 52 + 60 + x + 69 + 70 + 26 + 81 + 949 68 = 497 + x9 612 = 497 + x x = 612 - 497 x = 115

 

Data in ascending order

26,  45,  52,  60,  69,  70,  81,  94,  115

Since the number of observations is odd,  the median is the   n + 12 th  observation Median =  9  + 12th observation = 5th observation

Hence, the median is  69.

Question
ICSEENIMA10018855

The table shows the distribution of the scores obtained by  160 shooters in a shooting competition. Use a graph sheet and draw an ogive for the distribution ( Take  2 cm = 10  scores on the  X-axis  and  2 cm = 20  shooters on the  Y-axis ).

Scores 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50  50 - 60 60 - 70 70 - 80 80 - 90 90 - 100
No. of 
shooters  
9 13 20 26 30 22 15 10 8 7

Use your graph to estimate the following:

(i) The median.

(ii) The interquartile range.

(iii) The number of shooters who obtained a score of more than 85 %.

Solution

WiredFaculty

( i )  Median =  n 2 th term =  1602 th term = 80th term

Through mark  80  on y-axis, draw a horizontal line which meets the ogive drawn at point  Q.

Through  Q,  draw a vertical line which meets the  x-axis at the mark of  43.

 Median =  43.

 

( ii ) Since the number of terms = 160

Lower quartile ( Q1 ) = 1604th term = 40th term =  28.Upper quartile ( Q3 ) = 3 x 1604th term = 120th term =  60. Inter-quartile  = Q3 - Q1                              = 60 - 28                             = 32.

 

( iii ) Since  85 %  scores  =  85 %  of  100 = 85

Through mark for  85  on  x-axis, draw a vertical line which meets the ogive drawn at point  B.

Through the point  B,  draw a horizontal line which meets the  y-axis at the mark of  150.

 Number of shooters who obtained more than  85 %  score = 160 - 150 =  10.

Scores f c.f.
0 - 10 9 9
10 - 20 13 22
20 - 30 20 42
30 - 40 26 68
40 - 50 30 98
50 - 60 22 120
60 - 70 15 135
70 - 80 10 145
80 - 90 8 153
90 - 100 7 160
  n = 160