Question

observation of a data are 5 28 15 10 15 8 24 add four more number so that so that mean and median of the data remain the same but mode increased by 1

Answer 1

Observation of raw data in ascending order = 5, 8, 10, 15, 15, 24, 28

Arithmetic Mean = Sum of all observations/Number of observations

= (5 + 8 + 10 + 15+ 15 + 24 + 28)/7

= 105/7

Arithmetic Mean = 15

Median = (N + 1)/2 th item

N = 7

= (7 + 1)/2 th item

= 8/2

= 4th item

4th item is 15

So, median is 15.

Mode (Z) is the value that occurs most frequently or maximum time.

In the above data, 15 is most occurring value. So, Mode (Z) is 15.

So, in the above data -

Arithmetic mean = 15

Median (M)= 15

Mode (Z) = 15

Now, we have to add four numbers so that the mean and median of the data remain the same and the mode increase by 1.

The required four numbers are 12, 16, 16 and 16

Now,

Observations are - 5, 8, 10, 12, 15, 15, 16, 16, 16, 24, 28

Arithmetic Mean = (5 + 8 + 10 + 12 + 15 + 15 + 16 + 16 + 16 + 24 + 28)/11

= 165/11

Arithmetic Mean = 15

Median = (N + 1)/2 th item

= (11+ 1)/2 th item

= 12/2 th item

= 6th item

6th item is 15, So, median is 15

Mode (Z) in the above data is 16, because 16 is occurring maximum number of times.

So, in the new set of observations -

Arithmetic Mean = 15

Median = 15

Mode (Z) = 16

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