MEAN MEDIAN MODE PROBLEMS ON SAT

Problem 1 :

Gracie regularly buys six different items at the grocery store. The average price of the items is $30. The price of five items are $7, $25, $36, $40 and $44. What is the price of the sixth item ?

Solution :

Average of 6 items = 30

Let x be the price of 6^th item.

(7 + 25 + 36 + 40 + 44 + x)/6 = 30

152 + x = 6(30)

152 + x = 180

x = 180 - 152

x = 28

So, the price of the sixth item is $28.

Problem 2 :

The table gives the distribution of weights to the nearest pound, for 50 lobsters harvest off the coast of Maine and 50 lobster harvested off the coast of Masschusetts

What is the mean weight in pounds, of all the harvested lobsters ?

a)  1.34    b)  1.45    c)  1.67    d) 1.78

Solution :

Mean

= [(20 + 30) + 2(20 + 15) + 3(8 + 5) + 4(2 + 0)] / (50 + 50)

= (50 + 70 + 39 + 8) / 100

= 167/100

= 1.67

So, the mean is 1.67

Problem 3 :

A local pizza restaurant advertises a service that delivers pizza within 15 minutes. The histogram above was produced by a customer who timed the restaurant's delivery service to the nearest minute for 15 deliveries. Based on the mean delivery time, in minutes, of the restaurant ?

a)  14.4   b)  14.8    c)  15.2    d) 15.6

Solution :

Mean = (12(2) + 13(3) + 14(2) + 15(5) + 16(1) + 17(2))/15

= (24 + 39 + 28 + 75 + 16 + 34) / 15

= 216/15

= 14.4 minutes

So, option a is correct.

Problem 4 :

The graph above shows the frequency distribution of a list of randomly generated integers between 20 and 26. what is the mean of the list of integers ?

a)  21.5   b)  22    c)  22.5   d)  23

Solution :

Mean

= (20(1) + 21 (3) + 22 (4) + 24(1) + 25(1)) /(1+ 3 + 4 + 1 + 1)

= (20+63+88+24+25) / 10

= 220/10

= 22

So, the answer is 22.

Problem 5 :

The table above gives the atomic mass, to the nearest amu, of 15 different elements. Based on the table, what is the median atomic mass in amu of these elements ?

Solution :

1, 4, 7, 9, 11, 12, 14, 16, 18, 22, 25, 28, 32, 38, 42

Median of mass :

Number of mass = 15 (odd)

Median element = (15 + 1)/2

= 16/2

= 8^th element

= 16 amu

So, the median is 16.

Problem 6 :

The dot plot above shows the sugar content (in grams) in eahc of the 11 most popular soft drinks in Japan.

What is the mode of the data set ?

a)  0   b)  23      c)  25    d)  30

Solution :

Mode is the most repeated value.

By observing the dot plot, the mode is 30 

Problem 7 :

A phone manufacturer is using two different factories to test a new product. The dotplots above show the number defects in 9 products from each factory. Which of the following correctly compares the mean number of defects in the products from each factory ?

a) the mean number of defects in the products from factory A  is greater.

b)  The mean number of defects in the products from factory B is greater.

c)  The mean number of defects in the products from factory A  and in factory B is the same.

d)  The relationship cannot be determined from the information.

Solution :

Mean of factory A :

= (2(1) + 3(2) + 4(4) + 5(1) + 7(1))/9

= (2+6+16+5+7) / 9

= 36/9

= 4

Mean of factory B :

= (0(1) + 2(1) + 3(2) + 4(4) + 5(1))/9

= (0 + 2 + 6 + 16 + 5) / 9

= 29/9

= 3.2

So,  the mean number of defects in the products from factory A  is greater.

Problem 8 :

The mean height of the 14 students in a particular class is 63 inches. The mean height of 21 students in another class is 68 inches. If these two classes are combined, what is the mean height in inches of the students in the combined class ?

a) 64.5    b)  65   c)  66    d)  66.5

Solution :

Total number of students in the first class = 14

Total number of students in the second class = 21

Mean = sum of values / total number of values

Sum of combined classes = 63(14) + 68(21)

= 882 + 1428

= 2310

Mean = 2310/(14 + 21)

= 2310/35

= 66

Problem 9 :

A food company hires an independent research agency to determine its product's shell life, the length of time it may be stored before it expires. Using random sample of 40 units of the product the research agency finds that the product's shelf has a range of 3 days. Which of following must be true about the units in the sample ?

a) All the units expired within 3 days

b) The unit with the longest shelf life took 3 days longer to expire than the unit with the shortest shelf life.

c) The mean shelf life of the units is 3 more than the median.

d) The median shelf life of the units is 3 more than the mean.

Solution :

The range of 3 days means the difference between the longest shelf life and the shortest shelf life among the units is 3. This could be 10 days vs 13 or 25 days vs 28 days. The range says nothing amount the mean or median. So, option  b is correct.