Question

Make a frequency distribution for the following: 75, 76, 77, 76, 77, 78, 78, 79, 72, 73, 74, 76, 77, 78, 75, 71, 77, 79 and 80.

1. Make a frequency distribution. (6 POINTS)
2. Is this unimodal?                         (3 POINTS)
3. Is this skewed to the right?         (3 POINTS)
4. Where is the central tendency? (3 POINTS)

Answer 1

(a)

Following is the frequency distribution:

Data, x	Frequency, f
71	1
72	1
73	1
74	1
75	2
76	3
77	4
78	3
79	2
80	1
Total	19

b:

Mode is the data value with highest frequency. Since data value 77 has highest frequency 4 so mode of the data set is 77.

c:

Following is the histogram of data:

Histogram shows that distribution is skewed to left

d:

Since distribution has skewness so median should be used as a measure of central tendency. There are 19 data values so median will be 10th data value of ordered data set. That is median is 77.