Question

We are going to calculate the mean, median, and mode for two sets of data. Please show your answer to one decimal place if necessary.

Here is the first data set.

26

53

85

63

59

85

74

75

88

83

20

1. what is the mean (¯xx¯) of this data set?
2. 
   
3. What is the median of this data set?
   
4. What is the mode of this data set?
5. 
   
6. Here is the second data set.
   

   85

   47

   43

   48

   42

   30

   71

   77

   77

   38

7. 
   
8. What is the mean (¯xx¯) of this data set?
9. 
   
10. What is the median of this data set?
11. 
    
12. What is the mode of this data set?

Answer 1

For first data

a. Mean value is

b. The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

20   26   53   59   63   74   75   83   85   85   88   

So, the median is 74 .

c. The mode of a set of data is the value in the set that occurs most often.

Ordering the data from least to greatest, we get:

20   26   53   59   63   74   75   83   85   85   88   

We see that the mode is 85 .

For second data

d. Mean value is

e. The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

30   38   42   43   47   48   71   77   77   85   

As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:

Median

f. The mode of a set of data is the value in the set that occurs most often.

Ordering the data from least to greatest, we get:

30   38   42   43   47   48   71   77   77   85   

We see that the mode is 77 .