Find the mean ,median ,and mode for the following data.
4, 6, 7, 9, 13, 12, 9, 9, 13, 9, 9, 7, 8
Answers
Answer:
Step-by-step explanation:
Find the mean of the set {2,5,5,6,8,8,9,11} .
There are 8 numbers in the set. Add them all, and then divide by 8 .
2 + 5 + 5 + 6 + 8 + 8 + 9 + 118=548=6.75
So, the mean is 6.75 .
Find the median of the set {2,5,8,11,16,21,30} .
There are 7 numbers in the set, and they are arranged in ascending order. The middle number (the 4 th one in the list) is 11 . So, the median is 11 .
Find the mode of the set {2,3,5,5,7,9,9,9,10,12} .
2 , 3 , 7 , 10 and 12 each occur once.
5 occurs twice and 9 occurs three times.
So, 9 is the mode.
Mean = 8.85
Median = 9
Mode = 9
Given: The following data.
4, 6, 7, 9, 13, 12, 9, 9, 13, 9, 9, 7, 8
To Find: The mean, median, and mode
Solution:
- The mean of a distribution can be found by finding the summation of the values in the distribution and dividing it by the total number of values.
- The median distribution depends on the number of values.
→ If number of values (N) is odd, median = ( N + 1 )/2 th value of
distribution
→ If the number of values (N) is even, we will get 2 medians,
median = ( N/2) th value and ( N/2 + 1 )th value of the distribution
- The mode of a distribution is the value that has a maximum frequency ( or occurs a maximum number of times) in the distribution.
Coming to the numerical, we have the data as,
4, 6, 7, 9, 13, 12, 9, 9, 13, 9, 9, 7, 8
Mean = ( 4 + 6 + 7 + 9 + 13 + 12 + 9 + 9 + 13 + 9 + 9 + 7 + 8 ) / 13
= 115 / 13
= 8.85
Median = ( N + 1 )/2 th value of distribution = ( 13 + 1 )/2 th value of
distribution
= 7th value of distribution [ as N = odd ]
= 9
Mode = 9 [ As frequency of '9' = 5 ]
Hence,
Mean = 8.85
Median = 9
Mode = 9
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