Question

Find the mean, median mode(s), range, standard deviation, and variance of the data: 21, 15, 16, 25, 13, 18 5, 3, 2, 6, 5, 2, 5 Eight car sales men sold cars at a dealership. Here is the distribution of cars sold last month: 6, 45, 52, 43, 48, 41, 50, and 48. Find the mean, median mode(s), range, standard deviation, and variance of the data: Which measure of central tendency best represents the data

Answer 1

Kindly check explanation

Explanation:

Given tbe data :

21, 15, 16, 25, 13, 18 5, 3, 2, 6, 5, 2, 5

Ordered data : 2, 2, 3, 5, 5, 5, 6, 13, 15, 16, 18, 21, 25

Mean, m = Σx /n

Σx = 136

n = sample size = 13

m = Σx / n = 136 / 13 = 10.46

Mode, = 5 (most frequently occurring with frequency of 5)

Median = 1/2(n+1)th term = 1/2(14) = 7th term = 6

Range = maximum - minimum = [25 - 2] = 23

Variance : (V) = Σ(x - m)²/n-1

V = [(2-10.46)^2 + (2-10.46)^2 + (3-10.46)^2 + (5-10.46)^2 + (5-10.46)^2 + (5-10.46)^2 + (6-10.46)^2 + (13-10.46)^2 + (15-10.46)^2 + (16-10.46)^2 + (18-10.46)^2 + (21-10.46)^2 + (25-10.46)^2] / (13-1)

= 745.2308 / 12

= 62.10

Standard deviation = sqrt(V) = sqrt(62.10) = 7.88

2.)

X : 6, 45, 52, 43, 48, 41, 50, 48

Reordered data, X: 6, 41, 43, 45, 48, 48, 50, 52

Mean, m = Σx /n

Σx = 333

n = sample size = 8

m = Σx / n = 333 / 8 = 41.625

Median = 1/2 (n+1)th term = 46.5

Range = 52 - 6 = 46

Mode = 48 (highest occurring frequency of 2)

Variance (V) = Σ(x - m)²/n-1

V = [(6-41.625)^2 + (41-41.625)^2 + (43-41.625)^2 + (45-41.625)^2 + (48-41.626)^2 + (48-41.625)^2 + (50-41.625)^2 + (52-41.625)^2] / 5

= 1541.862251 / 7

= 220.27

Standard deviation = sqrt(Variance)

Standard deviation = sqrt(220.26603)

Standard deviation = 14.84

The median