Question

Q1. Find the median of :
a. 21, 21, 22, 23, 23, 24, 24, 24, 24, 25 and 25
b. 3.2, 4.8, 5.6, 7.3, 8.9 and 9.1
c. 80, 48, 66, 61, 75, 52, 45 and 70
Q2. Find the mean and the median of :
a. 10, 12, 12, 15, 15, 17, 18, 18, 18 and 19
b. 0.5, 5.6, 3.8, 4.9, 2.7 and 4.4
c. 5, 8, 10, 11, 13, 16, 19 and 20

Answer 1

Answer:

q1

a. 256

b. 38.9

c. 475

q2

a.

Answer 2

SOLUTION :

[1]

• (a) To find the median of : 21, 21, 22, 23, 23, 24, 24, 24, 24, 25 and 25

Here,

• The numbers are already in ascending order.

• Number of observations, n = 10

As the number of observations is an even number, the the median will be the average of (n/2) th and {(n/2) + 1}th term i.e. the average of 5th and 6th terms.

____________

• ★ Median = (5th term + 6th term) / 2

➨ Median = (24 + 24)/2

➨ Median = 48/2

➨ Median = 24

• Hence, the required median of the observation is 24

______________________________

• (b) To find the median of : 3.2, 4.8, 5.6, 7.3, 8.9 and 9.1

Here,

• The numbers are already in ascending order.

• Number of observations, n = 6

As the number of observations is an even number, the the median will be the average of (n/2) th and {(n/2) + 1}th term i.e. the average of 3rd and 4th terms.

____________

• ★ Median = (3rd term + 4th term) / 2

➨ Median = (5.6 + 7.3)/2

➨ Median = 12.9/2

➨ Median = 6.45

• Hence, the required median of the observation is 6.45

______________________________

• (c) To find the median of : 80, 48, 66, 61, 75, 52, 45 and 70

Here,

• Number of observations, n = 8

• Arranging the numbers in ascending order : 45, 48, 52, 61, 66, 70, 75, 80

As the number of observations is an even number, the the median will be the average of (n/2) th and {(n/2) + 1}th term i.e. the average of 4th and 5th terms.

____________

• ★ Median = (4th term + 5th term) / 2

➨ Median = (61 + 66)/2

➨ Median = 127/2

➨ Median = 63.5

• Hence, the required median of the observation is 63.5

____________________________________________

[2]

• (a) To find the Mean and Median of : 10, 12, 12, 15, 15, 17, 18, 18, 18 and 19

❒ Calculation of Mean :-

Here,

• Sum of the observations = 10 + 12 + 12 + 15 + 15 + 17 + 18 + 18 + 18 + 19 = 154

• No. of observations = 10

____________

• ★ Mean = Sum of the observations / No. of observations

➨ Mean = 154/10

➨ Mean = 15.4

• Hence, the Mean of the observations is 15.4

❒ Calculation of Median :-

Here,

• The observations are already in ascending order.

• No. of observations, n = 10

As the number of observations is an even number, the the median will be the average of (n/2) th and {(n/2) + 1}th term i.e. the average of 5th and 6th terms.

____________

• ★ Median = (5th term + 6th term) / 2

➨ Median = (15 + 17)/2

➨ Median = 32/2

➨ Median = 16

• Hence, the Median of the observations is 16

______________________________

• (b) To find the Mean and Median of : 0.5, 5.6, 3.8, 4.9, 2.7 and 4.4

❒ Calculation of Mean :-

Here,

• Sum of the observations = 0.5 + 5.6 + 3.8 + 4.9 + 2.7 + 4.4 = 21.9

• No. of observations = 6

____________

• ★ Mean = Sum of the observations / No. of observations

➨ Mean = 21.9/6

➨ Mean = 3.65

• Hence, the Mean of the observations is 3.65

❒ Calculation of Median :-

Here,

• Arranging the observations in ascending order : 0.5, 2.7, 3.8, 4.4, 4.9 and 5.6

• No. of observations, n = 6

As the number of observations is an even number, the the median will be the average of (n/2) th and {(n/2) + 1}th term i.e. the average of 3rd and 4th terms.

____________

• ★ Median = (3rd term + 4th term) / 2

➨ Median = (3.8 + 4.4)/2

➨ Median = 8.2/2

➨ Median = 4.1

• Hence, the Median of the observations is 4.1

______________________________

• (c) To find the Mean and Median of : 5, 8, 10, 11, 13, 16, 19 and 20

❒ Calculation of Mean :-

Here,

• Sum of the observations = 5 + 8 + 10 + 11 + 13 + 16 + 19 + 20

• No. of observations = 8

____________

• ★ Mean = Sum of the observations / No. of observations

➨ Mean = 102/8

➨ Mean = 12.75

• Hence, the Mean of observations is 12.75

❒ Calculation of Median :-

Here,

• The observations are already in ascending order.

• No. of observations, n = 8

As the number of observations is an even number, the the median will be the average of (n/2) th and {(n/2) + 1}th term i.e. the average of 4th and 5th terms.

____________

• ★ Median = (4th term + 5th term) / 2

➨ Median = (11 + 13)/2

➨ Median = 24/2

➨ Median = 12

• Hence, the Median of the observations is 12