Observations of a raw data are 5, 28, 15, 10, 15, 8, 24. Add four more numbers so that mean and median of the data remain the same, but mode increases by 1.
Answers
Answer:
Step-by-step explanation:
Arranging the data in ascending order = 5, 8, 10, 15, 15, 24, 28
Total number of observations = N = 7
Mean = Sum of all observations/Number of observations
= (5 + 8 + 10 + 15+ 15 + 24 + 28)/7
= 105/7 = 15
Mean = 15
Median = (N + 1)/2
= (7 + 1)/2
= 4
Since, 4th item is 15 so median is 15.
In the given data, 15 is most occurring value. Therefore, mode is 15. ( As mode (Z) is the frequently occcuring value)
Arithmetic mean = 15
Median (M)= 15
Mode (Z) = 15
Adding four numbers so that the mean and median of the data remain the same and the mode increases by 1.
The required four numbers will be 12, 16, 16 and 16
Thus the new observations - 5, 8, 10, 12, 15, 15, 16, 16, 16, 24, 28
Mean = (5 + 8 + 10 + 12 + 15 + 15 + 16 + 16 + 16 + 24 + 28)/11
= 165/11
= 15
Median = (N + 1)/2 th item
= (11+ 1)/2 th item
= 6th item
Since, 6th item is 15, So, median is 15
Mode (Z) in the above data is 16, as 16 is occurring the maximum number of times.
Therefore, Mean = 15, Median = 15 and Mode (Z) = 16
Answer:
Step-by-step explanation:
Arranging the data in ascending order = 5, 8, 10, 15, 15, 24, 28
Total number of observations = N = 7
Mean = Sum of all observations/Number of observations
= (5 + 8 + 10 + 15+ 15 + 24 + 28)/7
= 105/7 = 15
Mean = 15
Median = (N + 1)/2
= (7 + 1)/2
= 4
Since, 4th item is 15 so median is 15.
In the given data, 15 is most occurring value. Therefore, mode is 15. ( As mode (Z) is the frequently occcuring value)
Arithmetic mean = 15
Median (M)= 15
Mode (Z) = 15
Adding four numbers so that the mean and median of the data remain the same and the mode increases by 1.
The required four numbers will be 12, 16, 16 and 16
Thus the new observations - 5, 8, 10, 12, 15, 15, 16, 16, 16, 24, 28
Mean = (5 + 8 + 10 + 12 + 15 + 15 + 16 + 16 + 16 + 24 + 28)/11
= 165/11
= 15
Median = (N + 1)/2 th item
= (11+ 1)/2 th item
= 6th item
Since, 6th item is 15, So, median is 15
Mode (Z) in the above data is 16, as 16 is occurring the maximum number of times.
Therefore, Mean = 15, Median = 15 and Mode (Z) = 16