We read your photo as:

A Sociologist collected a sample of eight house and recorded the number of children in each house hold. The numbers are as follows: 2, 4, 3, 5, 1, 4, 3, 2. Find the Sample mean, mean deviation, Sample variency and the Sample standard deviation.

Mathematics

ScanSolve AI Answer

Step-by-step solution

4 steps

Here are the calculations for the given data: 2,4,3,5,1,4,3,22, 4, 3, 5, 1, 4, 3, 2.
The number of observations is n=8n = 8.

  1. Calculate the sample mean (xˉ\bar{x}).

    The formula for the sample mean is xˉ=∑xin\bar{x} = \frac{\sum x_i}{n}.

    ∑xi=2+4+3+5+1+4+3+2=24\sum x_i = 2 + 4 + 3 + 5 + 1 + 4 + 3 + 2 = 24 xˉ=248=3\bar{x} = \frac{24}{8} = 3

    The sample mean is 3\boxed{\text{3}}.

  2. Calculate the mean deviation (MD).

    The formula for the mean deviation is MD=∑∣xi−xˉ∣nMD = \frac{\sum |x_i - \bar{x}|}{n}.
    First, find the absolute differences from the mean:
    ∣2−3∣=1|2 - 3| = 1
    ∣4−3∣=1|4 - 3| = 1
    ∣3−3∣=0|3 - 3| = 0
    ∣5−3∣=2|5 - 3| = 2
    ∣1−3∣=2|1 - 3| = 2
    ∣4−3∣=1|4 - 3| = 1
    ∣3−3∣=0|3 - 3| = 0
    ∣2−3∣=1|2 - 3| = 1

    ∑∣xi−xˉ∣=1+1+0+2+2+1+0+1=8\sum |x_i - \bar{x}| = 1 + 1 + 0 + 2 + 2 + 1 + 0 + 1 = 8 MD=88=1MD = \frac{8}{8} = 1

    The mean deviation is 1\boxed{\text{1}}.

  3. Calculate the sample variance (s2s^2).

    The formula for the sample variance is s2=∑(xi−xˉ)2n−1s^2 = \frac{\sum (x_i - \bar{x})^2}{n-1}.
    First, find the squared differences from the mean:
    (2−3)2=(−1)2=1(2 - 3)^2 = (-1)^2 = 1
    (4−3)2=(1)2=1(4 - 3)^2 = (1)^2 = 1
    (3−3)2=(0)2=0(3 - 3)^2 = (0)^2 = 0
    (5−3)2=(2)2=4(5 - 3)^2 = (2)^2 = 4
    (1−3)2=(−2)2=4(1 - 3)^2 = (-2)^2 = 4
    (4−3)2=(1)2=1(4 - 3)^2 = (1)^2 = 1
    (3−3)2=(0)2=0(3 - 3)^2 = (0)^2 = 0
    (2−3)2=(−1)2=1(2 - 3)^2 = (-1)^2 = 1

    ∑(xi−xˉ)2=1+1+0+4+4+1+0+1=12\sum (x_i - \bar{x})^2 = 1 + 1 + 0 + 4 + 4 + 1 + 0 + 1 = 12 s2=128−1=127≈1.714s^2 = \frac{12}{8-1} = \frac{12}{7} \approx 1.714

    The sample variance is 127≈1.714\boxed{\frac{12}{7} \approx 1.714}.

  4. Calculate the sample standard deviation (ss).

    The formula for the sample standard deviation is s=s2s = \sqrt{s^2}.

    s=127≈1.7142857≈1.309s = \sqrt{\frac{12}{7}} \approx \sqrt{1.7142857} \approx 1.309

    The sample standard deviation is 127≈1.309\boxed{\sqrt{\frac{12}{7}} \approx 1.309}.

Was this helpful?

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp