a data is given below in which 1 no. was missed by the observer 96,98,75,20,102,100, ...... , 75. If the median of the data is 95. find the missing no. PLz someone send fast
Answers
Answer:
Step-by-step explanations
First thing we need tio do is to put the data in increasing order. This is needed to calculate the median:
30
,
31
,
32
,
33
,
34
,
35
,
35
,
36
,
37
,
39
Now we can calculate the parameters of this set:
Mean:
¯
x
=
30
+
31
+
32
+
33
+
34
+
35
+
35
+
36
+
37
+
39
10
=
342
10
=
34.2
Median
To calculate the median we need to take "middle" elements in an ordered set. If the set has an odd number of elements, then there is only one middle element, otherwise there are 2 such elements and median is the mean of those elements.
To find the middle elements we can cross out elements at both ends of the set until only 1 or 2 remain uncrossed:
30
,
31
,
32
,
33
,
34
,
35
,
35
,
36
,
37
,
39
30
,
31
,
32
,
33
,
34
,
35
,
35
,
36
,
37
,
39
30
,
31
,
32
,
33
,
34
,
35
,
35
,
36
,
37
,
39
30
,
31
,
32
,
33
,
34
,
35
,
35
,
36
,
37
,
39
There are 2 uncrossed elements, so their mean is the median:
M
e
=
34
+
35
2
=
69
2
=
34.5
Mode is the element which occurs the most times in the set. Here it is
35
.
Range is the difference between the smallest and the largest element:
r
=
39
−
30
=
9
20,75,75,96,98,100,102....and x, ur missing number...and if the median is 95.....being that u have 8 numbers, the median can be found by taking the 2 middle numbers and dividing by 2. So lets make our missing number (x) a middle number...and use it to find the median, which is 95
(96 + x) / 2 = 95
96 + x = 95 * 2
96 + x = 190
x = 190 - 96
x = 94
check...
20,75,75,94,96,98,100,102
median is : (94 + 96) / 2 = 190/2 = 95 (correct)