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Paraphin [41]
3 years ago
10

​Recently, a random sample of 13-18 year olds was​ asked, "How much do you currently have in​ savings?" The data in the table re

present the responses to the survey. Approximate the mean and standard deviation amount of savings.

Mathematics
1 answer:
Sonbull [250]3 years ago
6 0

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

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Step-by-step explanation:

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