Question

Weekly expenses of students taking a business mathematics class are shown in the below table. Complete parts a through d below.

Weekly expenses of students
8888	4141	7676	155155	6666	8787	9393	8181	5454	7575	8787	9898	8989
9191	8787	9595	101101	9595	8080	9494	5757	7676	8282	8484	105105	124124

a. Find the mean.

The mean is

nothing .

​(Round to the nearest whole number as​ needed.)

b. Find the median.

The median is

nothing .

c. Find the mode. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

The​ mode(s) is/are

nothing .

​(Use commas to separate answers as​ needed.)

B.

There is no mode.

d. Write a statement about the data set based on your findings. Choose the correct answer below.

A.

Only the mean and mode are very close so they give a realistic view of the average of the data.

B.

Only the median and mode are very close so they give a realistic view of the average of the data.

C.

Only the mean and median are very close so they give a realistic view of the average of the data.

D.

The​ mean, median, and mode all equal the same​ value, thus, they each give a realistic view of the average of the data.

Answer 1

( a ) Mean :

The mean of a data set is the sum of the terms divided by the total number of terms.

Mean=Sum of terms / Number of terms

Sum of terms = 88 + 41 + 76 + 155 + 66 + ⋯+ 124 = 2261

Number of terms = 26

Mean = 2261 / 26

= 86.9615

= 87

( b ) Median :

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:

41   54   57   66   75   76   76   80   81   82   84   87   87   87   88   89   91   93   94   95   95   98   101   105   124   155   

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 = (87+87) / 2 = 87

Median = 87

( c ) Mode :

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:

41   54   57   66   75   76   76   80   81   82   84   87   87   87   88   89   91   93   94   95   95   98   101   105   124   155   

We see that the mode is 87 .

d) Option (D)

The​ mean, median, and mode all equal the same​ value, thus, they each give a realistic view of the average of the data.