The mean of 40 items is 35. Later on, it was discovered that two items were misread as 36 and 29 instead of 63 and 22. Find the correct mean.
Solution:
Mean of 40 items = 35
Total of 40 items = 35 × 40 = 1400
Difference between two items which were wrongly read = (63 + 22) – (36 + 29)
= 85 – 65
= 20
Here,
Actual total = 1400 + 20 = 1420
Correct mean = 1420/40 = 35.5
Therefore, the correct mean is 35.5.
The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x.
29, 32, 48, 50, x, x + 2, 72, 75, 87, 91.
Solution:
N = 10 which is even
Median = ½ [n/2 th + (n/2 + 1)th term]
63 = ½ [10/2th + (10/2 + 1)th term]
63 = ½ (5th + 6th terms)
63 = ½ (x + x + 2)
63 × 2 = 2x + 2
2x = 126 – 2 = 124
By division
x = 124/2 = 62
Hence, the value of x is 62.
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