Question

Find the median of the following data:
(a) 73, 52, 56, 51, 42, 75, 53, 40
(b) 12, 9, 8, 7, 6, 2, 15, 13, 11, 10, 16 ​

Answer 1

Answer:

a. 52.5

b. 10

Step-by-step explanation:

Median

Ordering a data set x1 ≤ x2 ≤ x3 ≤ ... ≤ xn from lowest to the highest value, the median is the numeric value separating the upper half of the ordered sample data from the lower half. If n is odd the median is the center value. If n is even the median is the average of the 2 center values.  

If n is odd the median is the value at position p where  

pn+12

x˜=xp

If n is even the median is the average of the values at positions p and p + 1 where  

p=n2

x˜=xp+xp+12

-

PLS. MARK ME AS THE BRAINLIEST. HOPE THIS HELPS.

Answer 2

Answer:

• (a) n = 52.5
• (b) n = 10

Step-by-step explanation:

• (a) 73, 52, 56, 51, 42, 75, 53, 40

Arranging the data in ascending order,

➥ 40, 42, 51, 52, 53, 56, 73, 75

➥ n = 8 (even)

$\sf Median = \frac{ (\frac{n}{2}) ^{th} \: observation + ( \frac{n}{2} + 1)^{th} \: observation }{2} \\ \\ \sf = \frac{( \frac{8}{2})^{th} \: observation + ( \frac{8}{2} + 1) ^{th} \: observation}{2} \\ \\ \sf = \frac{4^{th} \: observation + {5}^{th} \: observation }{2} \\ \\ \sf = \frac{52 + 53}{2} = \frac{105}{2} = 52.5$

• (b) 12, 9, 8, 7, 6, 2, 15, 13, 11, 10, 16

Arranging the data in ascending order,

➥ 2, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16

➥ n = 11 (odd)

$\sf Mean = value \: of \bigg( \frac{n + 1}{2} \bigg)^{th} \: observation \\ \\ \sf = \bigg( \frac{11 + 1}{2} \bigg ) ^{th} observation \\ \\ \sf = {6}^{th} observation \\ \\ \sf = 10$