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 dotplot 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.