Question

​​

The following table shows a sample of the amount spent for lunch by 8 students

Lunch Spending ($) = xi
28
10
1
15
8
6
10
6

1. Calculate the sample mean amount spent for lunch. Use the correct statistical symbol to identify your answer.
2. This sample is (Circle one): Unimodal   Bimodal   Multi-Modal
3. What is/are the mode(s) for this sample?
4. What is the median of this sample?
5. Like most colleges, City College calculates a student’s Grade Point Average (GPA) by weighting each grade based on the number of units in the class. The following scale is used to convert letter grades into a quantitative variable:

A = 4

B = 3

C = 2

D = 1

F = 0

George’s transcript shows the following grades.

Class	Units	Grade
English	3	B
Biology	4	C
Geography	3	B
Weightlifting	1	A
Statistics	4	A
German	5	F

Calculate George’s GPA.

Answer 1

Problem 1

i)

Sample mean=Sum of observations/Number of observations

Sample mean=(28+10+1+15+8+6+10+6)/8=$10.50

ii)

Let us find the frequency of each amount spent

Amount Spent	Frequency
1	1
6	2
8	1
10	2
15	1
28	1

Highest frequency is 2.

It happens two times i.e. for amount spent of $6 and $10

So, data has two modes namely $6 and $10.

We can say that data is Bi-modal.

iii)

First we arrange data in ascending order.

1, 6, 6, 8,10, 10, 15, 28

Since number of observations is even, we take average of two middle most terms (4th and 5th) i.e. 8 and 10 to calculate median.

Median=(8+10)/2=$9

Problem 2

Georges GPA will be weighted average of George's score

Class	Units	Grade	Grade score	Unit*Grade Score
English	3	B	3	9
Biology	4	C	2	8
Geography	3	B	3	9
Weightlifting	1	A	4	4
Statistics	4	A	4	16
German	5	F	0	0
Sum	20			46

GPA=46/20=2.30