Question

Observations of a raw data are 5,28,15,10,15,8,24. Add four more numbers so that the mean and median of the data remain the same, but mode increases by 1.

Answer 1

The raw data is 5, 28, 15, 10, 15, 8, 24. We have to add four more numbers in this way that mean and median will remain same but mode will increase by 1.

In this data our mean is (5 + 28 + 15 + 10 + 15 + 8 + 24)/7 = 105/7 = 15.

And if we take the order of the data we get 5, 8, 10, 15, 15, 24, 28.

So, our median value is the middle most value which is 15.

and, Mode = 28 ( highest value)

Now we are adding 4 more data. At first we add 29 ( to get the mode we required). then we add 1 ( median and mean will be constant for adding 1).

We need 2 data more. So, we add 15, 15.

Now the data becomes 1, 5, 8, 10, 15, 15, 15, 15, 24, 28, 29, where mean = 15, mode = 29 and median = 15.(ans.)