Question

The mean of 1, 7, 5, 3, 4 and 4 is m. The observations 3, 2, 4, 2, 3, 3 and p have the mean (m – 1). Find the median of this set of data.

(a) 4 

(b) 2.5 

(c) 3 

(d) 5

Answer 1

(c) 3

m = \(\frac{1+7+5+3+4+4}{6}=\frac{24}{6}=4\)

Now mean of 3, 2, 4, 2, 3, 3 and p is (4 –1) = 3

∴ \(\frac{3+2+4+2+3+3+p}{7}=3\)

⇒ \(\frac{17+p}{7}\) = 3 ⇒ 17 + p = 21 ⇒ p = 4

∴ The observations are 3, 2, 4, 2, 3, 3 and 4.

Arranged in ascending order, the numbers are 2, 2, 3, 3, 3, 4, 4.

Median = \((\frac{7+1}{2})\)th value = 4th value = 3