Question

Student #	Grade (Marks)
1	89.2
2	86.4
3	83.5
4	81.1
5	78.2
6	73.9	BINS
7	64.3	60
8	71.7	70
9	65.5	80
10	66.2	90
11	72.4	100
12	67.5
13	85
14	86.9
15	83.7
16	82.7
17	81
18	80.9
19	83
20	82.2
21	81
22	77.6
23	72.9
24	61.2
25	66.9
26	70.8
27	65.2
28	55.9
29	71.8
30	85.5

An Economics professor is trying to investigate the distribution of the grades of the students in his class.

The data represents the grades of 30 randomly selected students.        

a. Using Excel, Find the summary statistics State the mean, median, mode, range and standard deviation of this sample data.

b. Comment of the shape of the Distribution by comparing the mean, median and mode in a) above ( Note: If mean< median

If mode < median < mean (Right skewed); If mean=median=mode (Symmetrical)

c. Using Excel, construct a frequency table, histogram and Ogive.

Use the bin range as: 60, 70, 80, 90 and 100.

Describe the shape of the histogram above. (Do not include Graph, Simply comment on the Shape.

d. Find the Quartiles (Q₁, Q_{2 ,} Q₃) using Excel . Interpret the Lower quartile (Q₁).

Answer 1

SOLUTION A: USING DATA ANALYSIS TOOL PACK WE HAVE

b) MEAN= 75.8

MEDIAN= 77.9

MODE=81

MODE > MEDIAN> MEAN

IT IS NEGATIVELY SKEWED OR LEFT SKEWED.

c) I'm including graph here just to show data is negatively skewed .

From The graph we can easily say the data is NEGATIVELY SKEWED.

d) By using QUARTILE FUNCTION of excel we have

QARTILE 1= 68.325

QARTILE 2= 68.325 77.9 WHICH IS ALSO CALLED MEDIAN OF DATA SET

QARTILE 3= 82.925

Interpretation Quartile 1 : In simplest term 25% of the data set will lie below 68.325.