Answer

Verified

374.1k+ views

**Hint:**We first express the given sample inputs in ascending order. Then we express the individual process and formulas to find sample range, sample mean, sample median, sample variance and sample standard deviation.

**Complete step by step solution:**

We have been given a sample of 11 discrete data $18,19,34,38,24,18,22,51,44,14,29$ and we need to find their sample range, sample mean, sample median, sample variance and sample standard deviation. In this sample $n=11$.

Arranging them in ascending order we get $14,18,18,19,22,24,29,34,38,44,51$. We consider the inputs as ${{x}_{i}},i=1(1)11$.

We express the mathematical formulas to find those attributes and put the values.

Sample range is equal to the difference between the highest and lowest value of the whole sample which is $51-14=37$.

Sample mean can be expressed as $\overline{x}=\dfrac{\sum{{{x}_{i}}}}{n}$. Putting the values, we get

\[\overline{x}=\dfrac{14+18+18+19+22+24+29+34+38+44+51}{11}=\dfrac{311}{11}=28.28\].

Sample median is expressed as the middle point of the ordered sample either in ascending or descending order. In this case of $14,18,18,19,22,24,29,34,38,44,51$, the median is 24.

Sample variance can be expressed as ${{\sigma }^{2}}=\dfrac{1}{n}\sum{{{x}_{i}}^{2}}-{{\left( \overline{x} \right)}^{2}}$. Now we find

\[\begin{align}

& \sum{{{x}_{i}}^{2}}={{14}^{2}}+{{18}^{2}}+{{18}^{2}}+{{19}^{2}}+{{22}^{2}}+{{24}^{2}}+{{29}^{2}}+{{34}^{2}}+{{38}^{2}}+{{44}^{2}}+{{51}^{2}} \\

& \Rightarrow \sum{{{x}_{i}}^{2}}=10243 \\

\end{align}\]

Putting the values, we get ${{\sigma }^{2}}=\dfrac{1}{11}\left( 10243 \right)-{{\left( 28.28 \right)}^{2}}=\dfrac{15952}{121}=131.83$.

Sample standard deviation can be expressed as \[\sigma =\sqrt{{{\sigma }^{2}}}=\sqrt{\dfrac{1}{n}\sum{{{x}_{i}}^{2}}-{{\left( \overline{x} \right)}^{2}}}\]. Putting the values, we get \[\sigma =\sqrt{131.83}=11.48\].

**Note:**

These all-required attributes are the measurement of central tendency and dispersion. The sample range, sample mean, sample median is part of central tendency and sample variance and sample standard deviation are part of dispersion.

Recently Updated Pages

Differentiate between Shortterm and Longterm adapt class 1 biology CBSE

How do you find slope point slope slope intercept standard class 12 maths CBSE

How do you find B1 We know that B2B+2I3 class 12 maths CBSE

How do you integrate int dfracxsqrt x2 + 9 dx class 12 maths CBSE

How do you integrate int left dfracx2 1x + 1 right class 12 maths CBSE

How do you find the critical points of yx2sin x on class 12 maths CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

The Buddhist universities of Nalanda and Vikramshila class 7 social science CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Name 10 Living and Non living things class 9 biology CBSE

Which are the Top 10 Largest Countries of the World?

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Who founded the Nalanda University 1 Mauryan 2 Guptas class 6 social science CBSE