The 4 Types of Measurement Scales: Nominal, Ordinal, Interval, Ratio

The answers to the following questionnaire items are based upon what scale of measurement? (4 responses)

What is your height? Interval scale 

What is your weight? Interval scale 

What is your occupation? Nominal scale 

How does this course compare with others you have taken? Ordinal scale 

(answers would be greater than, less than, equal to, etc.)

According to the table below, about what percentage of the flights had 19 or fewer empty seats?

about 71% 

Number of empty seats	Frequency
0 up to 5	3
5 up to 10	8
10 up to 15	15
15 up to 20	18
20 up to 25	12
25 up to 30	6

Complete this frequency distribution.

Number of empty seats	F	RF
0 up to 5	3	0.088
5 up to 10	1	.03
10 up to 15	8	0.235
15 up to 20	5	.15
20 up to 25	18	0.53
Total	34	1

Ratio level data are the “lowest level” of measurement and the data must be mutually exclusive. False 

The midpoint of 0 up to 5 class is

2

4

2.5

0

Midpoint 

All-Time Box Office Revenues Aggregated by Months (used for questions 5 – 7)

Rank	Month	Gross	Movies Tracked
1	February, 2009	796,343,640	161
2	February, 2010	745,693,066	173
3	February, 2008	659,270,466	193
4	February, 2004	666,141,251	201
5	February, 2007	693,647,238	176
6	February, 2003	613,460,961	207
7	February, 2005	692,957,988	185
8	February, 2006	652,426,175	193
9	February 2002	529,353,345	98

Calculate the mean for the gross revenues.

Mean (Gross Revenues) =  =   = 672,142,792.2222 

Calculate the mean for the Movies tracked.

Mean (Movies Tracked) =  = 176.3333 

Calculate the standard deviation for the movies tracked.

(161− 176.3333 ) 2 = (-15.3333) 2 = 235.1101 

(173− 176.3333 ) 2 = (-3.3333) 2 = 11.1109 

(193− 176.3333 ) 2 = (16.6667) 2 = 277.7789 

(201− 176.3333 ) 2 = (24.6667) 2 = 608.4461 

(176− 176.3333 ) 2 = (-0.3333) 2 = 0.1111 

(207− 176.3333 ) 2 = (30.6667) 2 = 940.4465 

(185− 176.3333 ) 2 = (8.6667) 2 = 75.1117 

(193− 176.3333 ) 2 = 16.6667) 2 = 277.7789 

(98− 176.3333 ) 2 = (-78.3333) 2 = 6136.1059 

Variance =  = 951.3333 

Standard deviation =  = 30.8437 

There are 14,233 members in the Energy and Advanced Manufacturing industry. Randomly, 233 were selected for an opinion survey. The 233 is a population.

True 

The ages for a sample of 10 women who have just given birth to their first child are 16, 25, 31, 19, 22, 20, 19, 25, 17, and 27. Compute each of the following descriptive measures:

the range

Range 

  31-16 

the variance

Step 1 - Find the mean of your terms. 

16+25+31+19+22+20+19+25+17+27=221 

Mean=  = 22.1 

Step 2 - Subtract the sample mean from each term 

(16−22.1) 2 = (-6.1) 2 = 37.21 

(25−22.1) 2 = (2.9) 2 = 8.41 

(31−22.1) 2 = (8.9) 2 = 79.21 

(19−22.1) 2 = (-3.1) 2 = 9.61 

(22−22.1) 2 = (-0.1) 2 = 0.01 

(20−22.1) 2 = (-2.1) 2 = 4.41 

(19−22.1) 2 = (-3.1) 2 = 9.61 

(25−22.1) 2 = (2.9) 2 = 8.41 

(17−22.1) 2 = (-5.1) 2 = 26.01 

(27−22.1) 2 = (4.1) 2 = 24.01 

∑ ( xi − ¯x    ) 2 = 206.9 

Variance =  =  = 22.9889 

the standard deviation 

sd =  = 

Paramount Studios has won the most Oscars than any other studio. Below is a chart indicating the movie and the box office receipts.

Titantic $600,788,188

Terms of Endearment $108,423,489

Forrest Gump $329,694,499

Ordinary People $ 54,766,923

Braveheart $ 75,609,945

What is the mean and SD for the movies above?

Mean (movies) =  =  = 233,856,608.80 

( 600,788,188 − 233,856,608.80 ) 2 = 1.346387838e+17 

( 108,423,489 − 233,856,608.80 ) 2 = 1.573346754e+16 

( 329,694,499 − 233,856,608.80 ) 2 = 9.184901198e+15 

( 54,766,923 − 233,856,608.80 ) 2 = 3.207311556e+16 

( 75,609,945 − 233,856,608.80 ) 2 = 2.504200660e+16 

Sum of differences 2 = 2.166722747e+17

Variance =  = 4.333445494e+16 

Sd =  =  = 208,169,293.95025

What is the probability that a film will make more than $220 million? 0.40 

What is the probability that a film will make between $150 million and $275 million? 0.20 

What is the probability that a film will make less than $350 million? 0.80 

Explain to me a concept from one of the first few chapters in your own words. Teach me as if I never understood the concept. You can write up to 100 words. Spelling, grammar, and precise content count.

Standard deviation refers to the statistical measure the level of dispersion or variability from the average. It basically measures the deviation from the mean and as such, it is known to be an effective measure of volatility. The higher the dispersion from the mean, the higher the standard deviation and vice versa. Without this concept, it would be very difficult for researchers to identify whether data is close to the average or spread out from it. It also provides room for the comparison of two data sets. For instance, just because two data sets have the same mean, it does not necessarily mean that the numbers are the same. This can only be determined by calculating their standard deviations. It is imperative to note that the standard deviation is derived from the square root of the variance of a given data set. The formula for population sd is given by  and sample sd is