Question

You are given data for a sample of 14 adults in Ohio indicating the number of times last week they ate in a fast food restaurant.

These data are as follows: 0, 1, 7, 2, 0, 0, 1, 3, 9, 3, 1, 0, 3, 4

1. a) Calculate the mean, median, mode, range, and standard deviation of the number of times per week these Ohio residents ate in a fast food restaurant.

2. b) Describe your results. Be sure to interpret the meaning of every one of these descriptive measures. Do the different measures lead you to different conclusions about the central tendency of these data? The dispersion? If so, describe how and why they lead you to different conclusions.

Answer 1

(a)

(i)

Mean = 34/14 = 2.4286

(ii)

Arranging numbers in ascending order:

0,0,0,0,1,1,1,2,3,3,3,4,7,9

n = 14

Median is(14+1)/2th item = average of 7th & 8th items= (1+2)/2 = 1.5

So,

median = 1.5

(iii)

mode = 4

since 0 appeared 4 times

(iv) Range= Maximum - Minimum =9 - 0= 9

(v)

x	x -	(x - )2
0	-2.4286	5.8980
1	- 1.4286	2.0408
7	4.5714	20.8980
2	- 0.4286	0.1837
0	- 2.4286	5.8980
0	- 2.4286	5.8980
1	-1.4286	2.0408
3	0.5714	0.3265
9	6.5714	43.1837
3	0.5714	0.3265
1	- 1.4286	2.0408
0	- 2.4286	5.8980
3	0.5714	0.3265
4	1.5714	2.4694
Total =		97.4286

Variance = s² =97.4286/13 = 7.4945

So,

Standard deviation =

(b)

(i)

Mean = 2.4286 is a single value that represents the center of the data.

(ii) Median = 1.5 is the middlemost item of the data,

(iii)Mode = 0, is the value with maximum frequency

(iv) Range = 9 gives the spread of data

(v) Standard deviation = 2.7376 gives the amount of dispersion of data around the mean.

Answer:
The different measures lead us to different conclusions about the central tendency of the data.

The different measures lead us to different conclusions about the dispersion of the data.

They lead to different measures due to large amount of outliers present in the data.