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Chapter 3: Q. 3.129 (page 123)

The data set has $250$ observations and has mean $100$ and standard deviation $16$ . Approximately how many observations lie between $52$ and $148$ .

Short Answer

Expert verified

$222$ observations lie between $52$ and $148$ .

Step by step solution

01

Given information

We are given that the data has $250$ and

Mean $x = 100$

Standard deviation $s = 16$ .

We have to find number of observations between $52$ and $148$ .

02

Simplify

According to Chebyshev's Rule

For any quantitative data set and any real number $k$ greater than or equal to $1$ , at least $1 - \frac{1}{k^{2}}$ of the observations lie within $k$ standard deviations to either side of the mean, that is, between $x - k (s)$ and $x + k (s)$

Now, according to given data

$x - k (s) = 52 100 - k (16) = 52 k = 3 x + k (s) = 148 100 + k (16) = 148 k = 3$

Therefore, number of observations between $52$ and $148$ are

$1 - \frac{1}{k^{2}} = 1 - \frac{1}{3^{2}} = 0.889 0.889 \times 250 \approx 222$

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We have provided simple data set for you to practices the basics of finding measures of center. For each data set determine the:

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