Question

actual times in seconds recorded when statistics students participated in a experiment to test their ability to determine when one minute had passed 53, 52, 75, 62, 68, 58, 49, 49

Answer 1

Explanation:

Hello!

To study time perception, 8 students measured one minute (counted to 60), the given data show the actual time (in seconds) it took each student to measure one minute:

53, 52, 75, 62, 68, 58, 49, 49

8 observations make this sample, n=8

You can summarize the observed data using descriptive statistics:

Central tendency measures:

Median (Me):

The median is the value that separates the sample in a half ( the bottom 50% from the top 50%). To calculate it you have to calculate its position:

(for even samples) PosMe: n/2= 8/2= 4

Then you arrange the data from least to greatest and identify the 4th value:

49, 49, 52, 53, 58, 62, 68, 75

Me= 53s

Mode (Md):

The mode is the most observed value, i.e. the value with the most absolute frequency:

In this data set, the only value that was observed more than once is 49, so that is the value of the mode

Md= 49s

Mean (X[bar]):

Is the average or expected value of the data set, it is always within the range of definition of the variable but it doesn't necessarily correspond to and observation. You calculate it as:

X[bar]= ∑X/n= (53+52+75+62+68+58+49+49)/8= 466/8= 58.25s

Measures of dispersion:

Range (R):

The is the difference between the minimum and maximum observations of the sample.

R= max - min = 75 - 49= 26s

Standard deviation (S):

It shows the variability between the values of the sample. A low standard deviation tells that the observations are close to the meanwhile a high standard deviation show that the values are further away from the mean.

∑X= 466

∑X²= 27772

`S= \sqrt{((1)/(n-1))[sumX^2-((sumX)^2)/(n) ]= \sqrt{((1)/(7) )[27772-((466)^2)/(8) ]} = \sqrt{(1255)/(14) } = 9.47s`

S= 9.47s

I hope this helps!