Question

A personal trainer is interested in the typical physical activity of her clients. She asked a sample of her customers how many hours of exercise they get each week, and recorded the data below.

Describe her findings using everything you've learned about measures of central tendency, measures of variability, and frequency distributions.
х = 2, 4, 5, 5, 7, 5, 3, 3, 4, 4
Include mean, mode, median, variance, standard deviation and type of distribution.

Answer 1

Mean = 4.2

Mode = 4 and 5

Median = 4

Variance, = 1.956

Standard deviation = 1.395

Explanation:

Given the data :

х = 2, 4, 5, 5, 7, 5, 3, 3, 4, 4

Ordered data : 2, 3, 3, 4, 4, 4, 5, 5, 5, 7

The mean, xbar = Σx / n ; n = sample size = 10

xbar = 42 / 10 = 4.2

The mode : 4 and 5 (most frequently occurring values) (3 frequency each) = BIMODAL

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

Median = 1/2(11)th term = 5.5 th term

Median = (5th + 6th term) /2 = (4 + 4) / 2 = 4

Variance , s² = Σ(x - xbar)²/(n-1)

Using a calculator :

Variance, s² = 1.956

Standard deviation, s = √variance = √s² = √1.956 = 1.395