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added Plotly.js to generate graphs
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‎content/exercises/graded-assignments/statistics-1/week-4-questions.md‎

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---
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title: Week 4 Statistics Graded Assignment Questions
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weight: 12
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tags:
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- statistics
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categories:
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- Statistics Graded Assignment
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series:
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- Statistics Graded Assignment
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---
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### Questions (1)–(6): Based on Table 4.1.G
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| Dealer's Location | OnePlus | BBK Electronics |
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| :-- | :-- | :-- |
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| Chennai | a | b |
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| Punjab | c | d |
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| Chennai | e | f |
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| Punjab | g | h |
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| Chennai | i | j |
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| Punjab | k | l |
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| Chennai | m | n |
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#### 1. What is the population standard deviation of sales of OnePlus? (Enter the answer correct to 2 decimal accuracy)
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{{< math/calc3 a=10 b=5 c=3 d=5 e=5 f=5 g=5 h=5 i=5 j=5 k=5 l=5 m=5 n=5 formula="a+b+c+d+e+f+g+h+i+j+k+l+m+n / 2" >}}
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**Solution:**
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Let $m_x$ and $\sigma_x$ be the mean and population standard deviation of sales of OnePlus respectively.
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$$
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m_x = \frac{a+c+e+g+i+k+m}{7}
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$$
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$$
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\sigma_x^2 = \frac{(a - m_x)^2 + (c - m_x)^2 + (e - m_x)^2 + (g - m_x)^2 + (i - m_x)^2 + (k - m_x)^2 + (m - m_x)^2}{7}
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$$
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Therefore, Population standard deviation of sales of OnePlus = $\sqrt{\sigma_x^2}$
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{{< math/calc3 a=10 b=5 formula="a + b * 2" >}}
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{{< math/calc3 x=2 y=3 z=4 formula="x * y + z" >}}
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---
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#### 2. What is the sample standard deviation of sales of BBK Electronics? (Enter the answer correct to 2 decimal accuracy)
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**Solution:**
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Let $m_y$ and $S_y$ be the mean and sample standard deviation of sales of BBK Electronics respectively.
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$$
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m_y = \frac{b+d+f+h+j+l+n}{7}
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$$
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$$
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S_y^2 = \frac{(b - m_y)^2 + (d - m_y)^2 + (f - m_y)^2 + (h - m_y)^2 + (j - m_y)^2 + (l - m_y)^2 + (n - m_y)^2}{7-1}
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$$
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Therefore, Standard deviation of sales of BBK Electronics = $\sqrt{S_y^2}$
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---
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#### 3. What is the sample co-variance between the sales of OnePlus and BBK Electronics? (Enter the answer correct to 2 decimal accuracy)
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**Solution:**
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Let $X$ = Sales of OnePlus
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$Y$ = Sales of BBK Electronics.
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$$
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Cov(X,Y) = \frac{\sum_{i=1}^{7}(x_i - m_x)(y_i - m_y)}{7-1}
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$$
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$$
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= \frac{(a - m_x)(b - m_y) + (c - m_x)(d - m_y) + (e - m_x)(f - m_y) + (g - m_x)(h - m_y) + (i - m_x)(j - m_y) + (k - m_x)(l - m_y) + (m - m_x)(n - m_y)}{6}
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$$
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---
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#### 4. What is the correlation coefficient between the sales of OnePlus and BBK Electronics? (Enter the answer correct to 2 decimal accuracy)
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**Solution:**
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Let $r$ be the correlation coefficient between the sales of OnePlus and BBK Electronics.
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$$
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r = \frac{Cov(X,Y)}{S_x \times S_y}
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$$
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where,
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Cov(X,Y) = Sample Covariance between sales of OnePlus and BBK Electronics.
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$S_x$ = Sample standard deviation of sales of OnePlus = $\sqrt{\frac{n}{n-1}} \sigma_x$ = $\sqrt{\frac{7}{6}} \sigma_x$
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$S_y$ = Sample standard deviation of sales of BBK Electronics.
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---
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#### 5. What can you say about the linear relationship between the sales of OnePlus and BBK Electronics? (More than one option can be correct)
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(a) Strong
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(b) Positive
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(c) Weak
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(d) Negative
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(e) Absence of linear relationship
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(f) Moderate
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**Solution:**
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- If $0.75 \leq r \leq 1$, then there is a strong and positive linear relationship.
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- If $0.5 < r < 0.75$, then there is a moderate and positive linear relationship.
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- If $0.25 < r < 0.5$, then there is a weak and positive linear relationship.
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- If $-0.25 < r < 0.25$, then there is absence of linear relationship.
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- If $-0.5 < r < -0.25$, then there is a weak and negative linear relationship.
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- If $-0.75 < r < -0.5$, then there is a moderate and negative linear relationship.
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- If $-1 < r < -0.75$, then there is a strong and negative linear relationship.
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---
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#### 6. Is the sales of OnePlus strongly influenced by the location of dealer?
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(a) Yes
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(b) No
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**Solution:**
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Let Chennai be represented by 0 and Punjab by 1.
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The Point Bi-serial correlation coefficient between the sales of OnePlus and the location of dealer is given by:
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$$
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r_{pb} = \frac{(\bar{Y_0} - \bar{Y_1})}{\sigma_x} \times \sqrt{p_0 \times p_1}
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$$
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where,
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$p_0$ = Proportion of Chennai dealers = $\frac{4}{7}$
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$p_1$ = Proportion of Punjab dealers = $\frac{3}{7}$
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$\bar{Y_0}$ = Mean sales of OnePlus in Chennai = $\frac{a+e+i+m}{4}$
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$\bar{Y_1}$ = Mean sales of OnePlus in Punjab = $\frac{c+g+k}{3}$
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$\sigma_x$ = Population standard deviation of sales of OnePlus
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$$
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r_{pb} = \frac{(\bar{Y_0} - \bar{Y_1})}{\sigma_x} \times 0.49487
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$$
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If $0.75 \leq |r_{pb}| \leq 1$, then the sales of OnePlus is strongly influenced by the location of dealer.
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Else, the sales of OnePlus is not strongly influenced by the location of dealer.
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---
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### Questions (7)–(11): Based on Table 4.2.G
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| Economic Conditions | Bright | Average | Dull | Borderline |
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| :-- | :-- | :-- | :-- | :-- |
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| Good | a | b | c | d |
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| Poor | e | f | g | h |
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#### 7. What proportion of total students are dull? (Enter the answer correct to 2 decimal accuracy)
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**Solution:**
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Proportion of dull students = $\frac{c+g}{a+b+c+d+e+f+g+h}$
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---
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#### 8. What proportion of total students are poor economic conditions? (Enter the answer correct to 2 decimal accuracy)
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**Solution:**
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Proportion of students having poor economic conditions = $\frac{e+f+g+h}{a+b+c+d+e+f+g+h}$
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---
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#### 9. What proportion of students of good economic conditions are borderline? (Enter the answer correct to 2 decimal accuracy)
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**Solution:**
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Required proportion = $\frac{d}{a+b+c+d}$
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---
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#### 10. What percentage of bright students are in poor economic conditions? (Enter the answer correct to 2 decimal accuracy)
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**Solution:**
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Required percentage = $(\frac{e}{a+e}) \times 100$
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---
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#### 11. What percentage of average students are in good economic conditions? (Enter the answer correct to 2 decimal accuracy)
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**Solution:**
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Required percentage = $(\frac{b}{b+f}) \times 100$
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---

‎content/notes/iit-madras/data-science-and-application/foundational-level/mathematics/week 1/aq1.11.md‎

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The image also provides context stating: "The domain and range of the function that is shown in Figure 1 are [m, x] and [n, y] respectively, where m, n, x, y ∈ ℝ."
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{{< math/geogebra id="azbxfs9y" width="600" height="600" >}}
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{{< math/geogebra id="azbxfs9y" width="600" height="300" >}}
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{{< plotly formula="Math.sin(x)" xmin="-6.28" xmax="6.28" step="0.05" title="y = sin(x)" xlabel="x" ylabel="y" >}}
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{{< plotly formula="x^2-5" xmin="-6.28" xmax="6.28" step="0.05" title="y = sin(x)" xlabel="x" ylabel="y" >}}
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{{< plotly formula="(Math.pow(x,2)) - 5" xmin="-6.28" xmax="6.28" step="0.05" title="y = sin(x)" xlabel="x" ylabel="y" >}}
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{{< math/geogebra id="fe9vckwu" width="600" height="300" >}}
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{{< math/geogebra id="qm9mevaj" width="400" height="300" >}}
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{{< plotly formula="x*x + 2*x + 1" xmin="-10" xmax="10" step="0.1" title="Quadratic: y = x² + 2x + 1" xlabel="x" ylabel="y" >}}
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A coordinate graph (Figure 1) is shown with several plotted points including (0, 9), (-4, 2), (3, 1), and (9, 6), suggesting there may be additional questions related to this graph that would follow this context.
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‎content/notes/iit-madras/data-science-and-application/foundational-level/mathematics/week 3/aq3.1.md‎

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weight: 31.5
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---
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{{< math/geogebra id="rbjh4eef" width="600" height="300" >}}
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{{< border >}}
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**Question 1:** Which of the graphs in Figure 1 represents the following function: $y = x^2 - x + 1$?

‎layouts/partials/question-cards.html‎

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<style>
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.question-card {
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border: 3px solid #e0e0e0;
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border: 2px solid #e0e0e0;
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border-radius: 8px;
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padding: 20px;
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background: #fff;
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box-shadow: 0 4px 6px rgba(0, 0, 0, 0.5);
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}
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.question-card h3 {
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margin: 0;

‎layouts/shortcodes/math/geogebra.html‎

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<!-- filepath: d:\Code\hextra-notes\layouts\shortcodes\math\geogebra.html -->
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{{ $materialID := .Get "id" | default "" }}
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{{ $width := .Get "width" | default "800" }}
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{{ $width := .Get "width" | default "800" }}
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{{ $height := .Get "height" | default "600" }}
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{{ $aspect := div (float $height) (float $width) | mul 100 }}
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{{ $sfsb := .Get "sfsb" | default "true" }}
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{{ $smb := .Get "smb" | default "false" }}
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{{ $stb := .Get "stb" | default "false" }}
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{{ $ai := .Get "ai" | default "false" }}
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{{ $sdz := .Get "sdz" | default "false" }}
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{{/* Engable Right Click, Zomming and Keboard Editing */}}
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{{ $rc := .Get "rc" | default "false"}}
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{{/* Show the Algebra Input Bar. */}}
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{{ $ai := .Get "ai" | default "false" }}
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{{/* Enable Shoft-Drag & Zoom */}}
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{{ $sdz := .Get "sdz" | default "false" }}
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{{/* Show the GeoGebra Menu Bar. */}}
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{{ $smb := .Get "smb" | default "false" }}
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{{/* Show the GeoGebra Toolbar. */}}
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{{ $stb := .Get "stb" | default "false" }}
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{{/* Show Toolbar Help */}}
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{{ $stbh := .Get "stbh" | default "false" }}
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{{/* Allow label dragging */}}
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{{ $Id := .Get "Id" | default "false" }}
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{{/* Show Reset icon (top-right) */}}
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{{ $sri := .Get "sri" | default "false" }}
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{{/* Show play button that starts the construction */}}
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{{ $ctl := .Get "ctl" | default "false" }}
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{{/* Show full-screen button. Make sure you alse add allowfullscreen to the iframe tag. */}}
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{{ $sfsb := .Get "sfsb" | default "false" }}
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{{/* Show zoom buttons */}}
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{{ $szb := .Get "szb" | default "false" }}
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{{ $sfbl := .Get "sfbl" | default "false" }}
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{{ $sri := .Get "sri" | default "false" }}
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{{ if not $materialID }}
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<p class="error">GeoGebra material ID is required.</p>
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{{ return }}
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{{ end }}
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{{ if not $materialID }}
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<p class="error">GeoGebra material ID is required.</p>
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{{ return }} {{ end }}
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<div class="ggb-responsive-container" style="--aspect:{{ $aspect }}%;">
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<iframe
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src="https://www.geogebra.org/material/iframe/id/{{ $materialID }}/width/{{ $width }}/height/{{ $height }}/border/888888/sfsb/{{ $sfsb }}/smb/{{ $smb }}/stb/{{ $stb }}/ai/{{ $ai }}/sdz/{{ $sdz }}/sfbl/{{ $sfbl }}/sri/{{ $sri }}"
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src="https://www.geogebra.org/material/iframe/id/{{ $materialID }}/width/{{ $width }}/height/{{ $height }}/border/888888/rc/{{ $rc }}/szb/{{ $szb }}/ctl/{{ $ctl }}/Id/{{ $Id }}/stbh/{{ $stbh }}/sfsb/{{ $sfsb }}/smb/{{ $smb }}/stb/{{ $stb }}/ai/{{ $ai }}/sdz/{{ $sdz }}/sfbl/{{ $sfbl }}/sri/{{ $sri }}"
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allowfullscreen
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loading="lazy"
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style="border: 1px solid #e4e4e4; border-radius: 4px"
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></iframe>
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</div>
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<style>
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.ggb-responsive-container {
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position: relative;
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width: 100%;
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padding-top: var(--aspect, 75%);
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max-width: 900px;
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margin: 1em auto;
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}
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.ggb-responsive-container iframe {
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position: absolute;
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top: 0; left: 0;
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width: 100%;
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height: 100%;
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border: 0;
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display: block;
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}
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.ggb-responsive-container {
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position: relative;
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width: 100%;
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padding-top: var(--aspect, 75%);
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max-width: 900px;
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margin: 1em auto;
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border: 1px solid #e4e4e4;
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border-radius: 4px;
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}
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.ggb-responsive-container iframe {
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position: absolute;
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top: 0;
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left: 0;
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width: 100%;
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height: 100%;
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border: 0;
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display: block;
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object-fit: cover;
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}
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</style>
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{{/* {{< math/geogebra id="abcd1234" width="700" height="500" sfsb="false" smb="true" stb="true" ai="true" sdz="false" sfbl="true" >}} */}}
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{{/* {{< math/geogebra id="abcd1234" width="700" height="500" sfsb="false"
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smb="true" stb="true" ai="true" sdz="false" sfbl="true" >}} */}}

‎layouts/shortcodes/math/graph.html‎

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<!-- filepath: d:\Code\hextra-notes\layouts\shortcodes\plotly.html -->
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{{ $id := printf "plotly_%d" now.UnixNano }}
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{{ $formula := .Get "formula" | default "Math.sin(x)" }}
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{{ $xmin := .Get "xmin" | default "-10" }}
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{{ $xmax := .Get "xmax" | default "10" }}
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{{ $step := .Get "step" | default "0.1" }}
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{{ $title := .Get "title" | default "Plotly Graph" }}
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{{ $xlabel := .Get "xlabel" | default "x" }}
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{{ $ylabel := .Get "ylabel" | default "y" }}
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<div id="{{ $id }}" style="width:100%;max-width:600px;height:400px;"></div>
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<script src="https://cdn.plot.ly/plotly-2.32.0.min.js"></script>
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<script>
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(function() {
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var x = [];
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var y = [];
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for (var i = Number({{ $xmin }}); i <= Number({{ $xmax }}); i += Number({{ $step }}) ) {
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x.push(i);
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try {
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y.push(eval("{{ $formula }}".replace(/x/g, "(" + i + ")")));
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} catch(e) {
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y.push(null);
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}
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}
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Plotly.newPlot("{{ $id }}", [{
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x: x,
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y: y,
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mode: 'lines',
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line: {color: '#0078d4'},
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name: "{{ $formula }}"
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}], {
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title: "{{ $title }}",
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xaxis: {title: "{{ $xlabel }}"},
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yaxis: {title: "{{ $ylabel }}"}
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}, {responsive: true});
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})();
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</script>
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{{/* {{< plotly formula="Math.sin(x)" xmin="-6.28" xmax="6.28" step="0.05" title="y = sin(x)" xlabel="x" ylabel="y" >}} */}}

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