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Example 17: The runs scored by 10 players of a cricket team are 39, 58, 124, 27, 17, 35, 28, 41, 23, 18

Find the median score.
Alternate Method
Solution: Number of observations, If the number of observations is n (even),

n = 10 (even)  n  n 

  th observation +  + 1 thobservation


2

Arranging them in ascending order Then, median = 2
2
17, 18, 23, 27, 28, 35, 39, 41, 58, 124  10  10 


  2   th observation +   2 + 1 thobservation
Mean of both middle terms So, median = 2
So, Median = mean of middle 5thobservation + 6thobservation
terms 28 and 35 = 2
28 35 63 28 35 63
+
+
.
.
= = = 31 5 = = = 31 5
2 2 2 2
Thus, the required median score is 31.5. Thus, the required median score is 31.5.
Practice Time 14A

1. Find mean of the following observations:
(a) 11, 9, 7, 10, 12, 8, 13 (b) 14, 16, 19, 25, 21, 15, 17, 25
(c) 23, 2, 0, −2, 19, 11, −3, 1, 17, 6
2. Find the mode of the following observations:
(a) 7, 3, 0, 2, 3, 5, 6, 2, 1, 4, 3 (b) 17, 13, 11, 11, 16, 17, 23, 17, 11, 15, 17, 20
(c) 14, 6, 12, 6, 11, 13, 14, 17, 6, 14, 12, 8, 3, 9, 14, 6, 14
3. Find median of the following observations:
(a) 6, 9, 10, 2, 17, 16, 11, 5, 12 (b) 3, −2, 0, 11, 6, −5, 8, 1, 7, 2
(c) 4, 6, 10, 6, 2, 8, 4, 3, 2, 4, 6
4. Find the mean of first five odd natural numbers.
5. Find the mean of first ten prime numbers.
6. Find the mean of all the factors of 10.
7. In last annual examination, Ramesh scored the following marks in 6 subjects.
72, 70, 81, 85, 80, 62
Find his arithmetic mean of marks obtained.
8. If the mean of (2x − 1), 3, 4 and 8 is (x + 1), then find the value of x.
9. The median of observations 11, 12, 14, 18, a + 2, 20, 22, 25, 61 arranged in ascending order is 21.
Find the value of a.
10. The mean of six numbers is 48. It was found later that one number 27 was wrongly written as 17.
Find the correct mean.
11. The mean of eight numbers is 108. It was found later that two numbers 19 and 21 were wrongly
written as 91 and 12. Find the correct mean.
12. The mean of five numbers is 45. If one of the numbers is excluded, the mean becomes 35. Determine
the excluded number.
13. The mean of seven numbers is 98. If one more number is included, then the mean becomes 88.
Determine the included number.
14. In a seven-a-side football tournament, the height of players of a team are 167 cm, 145 cm, 140 cm, 150
cm, 155 cm, 160 cm and 168 cm. Find the mean, mode and median height of a player of that team.

315 Data Handling