#### 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 (5^{th} + 6^{th} 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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