The mean of 1, 3, 4, 5, 7, 4 is m. The numbers 3, 2, 2, 4, 3, 3, p have mean m − 1 and median q. Then, p + q =A. 4B. 5C. 6D. 7

First data is:

1, 3, 4, 5, 7, 4

Given, mean = m

And we know,

Mean …[1]

No of observations = 6

Sum of all observations = 1 + 3 + 4 + 5 + 7 + 4 = 24

Hence,

Mean

m = 4 …[2]

Second data is :

3, 2, 2, 4, 3, 3, p

No of observations = 7

Sum of observations = 3 + 2 + 2 + 4 + 3 + 3 + p = 17 + p

Given,

Mean = m - 1

Using [1]

21 = 17 + p

p = 4 …[3]

Hence, series is 3, 2, 2, 4, 3, 3, 4

For median, let us write our data in increasing order

2, 2, 3, 3, 3, 4, 4,

Also, as the no of terms in this data is odd

We know that if there are odd number of terms in a data, then the median of data is term. Where n is no of terms

n = 7

median = 4th term = 3

q = 3 …[4]

From [3] and [4]

p + q = 4 + 3 = 7

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