Find the value of k if the mean of the following data is 17.
xi1014182125fi1015k99
Average or mean value of a given number of observations is the sum of all the observations divided by the total number of observations.
xi1014182125fi1015k99xifi10021018k189225
Mean =∑xifi∑fi
∑xifi=100+210+18k+189+225=724+18k
∑fi=10+15+k+9+9=43+k
Given that mean = 17
We can write,
17=724+18k43+k
⇒724+18k = 17×(43+k)
⇒18k−17k=731−724
⇒k=7