Question

Below are monthly rents paid by 30 students who live off campus.

590 590 590 790 560 450 550 890 600
480 580 520 420 600 510 520 710 775
460 480 620 550 570 365 590 660 680
700 580 630

Required:
a. Find the mean, median, mode, and standard deviation.
b. Which measure or measures of central tendency are most appropriate for this data set?
c. Do the measures of central tendency agree?

Answer 1

Mean = 587

Median = 585

Mode = 590

Standard deviation = 112.538

The mean and the median

Yes, both mean and median have close values

Explanation:

Given the data:

365, 420, 450, 460, 480, 480, 510, 520, 520, 550, 550, 560, 570, 580, 580, 590, 590, 590, 590, 600, 600, 620, 630, 660, 680, 700, 710, 775, 790, 890

The mean, m = Σx / n = 17610 / 30

Mean = 587

The median = 1/2(n+1)th term

Median = 1/2(31)th term

Median = 15.5th = (580+590) / 2 = 585

The mode = 590 (observation with highest frequency, 4)

Standard deviation, s = √Σ(x-m)²/(n-1)

s = 112.538