Question

Following are the lives in hours of 15 pieces of the components of aircraft engine. Find the median:
715, 724, 725, 710, 729, 745, 694, 699, 696, 712, 734, 728, 716, 705, 719

Answer 1

SOLUTION :  

Given : Lives in hours of 15 pieces are = 715, 724, 725, 710, 729, 745, 694, 699, 696, 712, 734, 728, 716, 705, 719

Arrange the above data in ascending order = 694, 696, 699, 705, 710, 712, 715, 716, 719, 721, 725, 728, 729, 734, 745

Here, n = 15 (odd)

Median = value of [(n+1)/2]th observation

= value of [(15 + 1)/2 ]th observation

= value  of (16/2)th observation

= value  of 8th observation

= 716

Hence, the Median is 716.

MEDIAN: Median is defined as the middle most or the Central observation , when the observations are arranged either in ascending or descending order of their magnitudes.

★★Median is that value of the given observation which divides it into exactly two parts.i.e 50% of the observations lie below the median and the remaining are above the median.

★★ Median of the data depends on the number of observations (n) .

i) If n is odd then median= value of [(n+1)/2]th observation

ii) If n is even then median= ½value of [ (n/2)th + (n/2 +1) th] observations.

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Answer :

The median is 716.

Step-by-step explanation :

Median -

It is defined as the middle observation or the observation which comes at centre when the observations are arranged in either ascending order or descending order.

Median is the value which differentiate observation into 50% - 50% each.

Median of the data depends upon the number of observations i.e., n.

● If n is odd then, median is the value of $\frac{(n+1)}{2}$th observation.

● If n is even then, median is the half of the value of $\frac{n}{2}+(\frac{n}{2}+1)$

Given, the lives in hours of 15 pieces of the component of aircraft engine -

$715,724,725,710,729,745,694,699,$ $712,696,734,728,716,705,719$

Arranging the given data in ascending order -

$694,696,699,705,710,712,715,716,$$719,721,725,728,729,734,745$

Here, the number of observations, n = 15 is odd.

Therefore,

Median = value of $\frac{(n+1)}{2}$th observation.

$\implies$ value of $\frac{(15+1)}{2}$th observation.

$\implies\:\:\frac{16}{2}$th observation.

$\implies$ value of 8th observation

$\implies$ 716