Question

​Recently, a random sample of 13-18 year olds was​ asked, "How much do you currently have in​ savings?" The data in the table represent the responses to the survey. Approximate the mean and standard deviation amount of savings.

Answer 1

Answer:

μ = 235.38

σ = 234.54

Step-by-step explanation:

Assuming the table is as follows:

$\left[\begin{array}{cc}Savings&Frequency\\\ 0-\ 199&339\\\ 200-\ 399&86\\\ 400-\ 599&55\\\ 600-\ 799&18\\\ 800-\ 999&11\\\ 1000-\ 1199&8\\\ 1200-\ 1399&3\end{array}\right]$

This is an example of grouped data, where a range of values is given rather than a single data point.  First, find the total frequency.

n = 339 + 86 + 55 + 18 + 11 + 8 + 3

n = 520

The mean is the expected value using the midpoints of each range.

μ = (339×100 + 86×300 + 55×500 + 18×700 + 11×900 + 8×1100 + 3×1300) / 520

μ = 122400 / 520

μ = 235.38

The variance is:

σ² = [(339×100² + 86×300² + 55×500² + 18×700² + 11×900² + 8×1100² + 3×1300²) − (520×235.38²)] / (520 − 1)

σ² = 55009.7

The standard deviation is:

σ = 234.54