KindiakMath

Baby Data Visualisation

Problem 1. A budget airline’s call centre logs the number of customer complaints received each working day over 20 consecutive days. The counts for the 20 days, in ascending order, are presented in a stem-and-leaf diagram below.

Legend: 1 | 6 represents 16 complaints

Represent the data using a box-and-whisker diagram.

(Click for Solution)

Solution. We first calculate Q0 = 16, Q4 = 52, and

Q2 = 0.5 × (31 + 33) = 32.

Furthermore,

Q1 = 0.5 × (26 + 27) = 26.5 and Q3 = 0.5 × (37 + 38) = 37.5.

Therefore, we draw the box-and-whisker diagram as follows.

Number of complaints

Problem 2. A retail bank records the value ($) of every cash withdrawal made at its ATMs over one business day. The results are presented in a histogram below.

Estimate the mean and the standard deviation value of the withdrawals in that day.

(Click for Solution)

Solution. We tabulate the frequency with the proxy mid-value.

Amount ($)Frequency, fMid-value, xfxfx2
0 ≤ x < 108540200
10 ≤ x < 2022153304950
20 ≤ x < 30322580020 000
30 ≤ x < 40283598034 300
40 ≤ x < 503045135060 750
50 ≤ x < 602255121066 550
60 ≤ x < 702065130084 500
70 ≤ x < 8018751350101 250
80 ≤ x < 901285102086 700
90 ≤ x ≤ 10089576072 200
Sum, Σ2009140531 400

Hence, we compute the mean \bar x and the standard deviation \sigma_x by

\displaystyle \bar x = \frac{\Sigma fx}{\Sigma f} = \frac{9140}{200} = 45.7\, \text{days}

and

\begin{aligned} \sigma_x &= \sqrt{ \frac{\Sigma fx^2}{\Sigma f} - \left( \frac{\Sigma fx}{\Sigma f} \right)^2 } \\ &= \sqrt{ \frac{531\, 400}{200} - \left( \frac{9140}{200} \right)^2 }\\ &\approx 22.8\, \text{days}. \end{aligned}

Problem 3. An online clothing retailer publishes the pictogram below to display quarterly sales on its investor webpage.

The sales in each quarter are denoted by the dollar amounts. Explain why the pictogram gives a misleading impression of the sales.

(Click for Solution)

Solution. Q3 has $4000 ÷ $1000 = 4 times the amount of sales as Q1, but is represented by a rectangle with area strictly larger than 4 times the area of the rectangle that represents Q1, misleading viewers that Q3’s earnings is more than 4 times the earnings of Q1.

Problem 4. An e-commerce logistics company tracks the average parcel delivery time (in days) each month. The data for one calendar year are presented in the line graph below.

Estimate the percentage decrease in average delivery time from January to August.

(Click for Solution)

Solution. The average delivery time in January is 4.2 days, while the average delivery time in August is 3.1 days. Hence, the percentage change is given by

\displaystyle \frac{3.1 - 4.2}{4.2} \times 100\% \approx -26.2\%.

Hence, the percentage decrease is approximately 26.2%.

Problem 5. The pie chart below shows a country’s electricity generation by source for a given year.

Calculate the angle of the sector that represents electricity generated by solar energy source.

(Click for Solution)

Solution. Since a full turn corresponds to 360°, 5% of a full turn corresponds to an angle of

5% × 360° = 0.05 × 360° = 18°.

—Joel Kindiak, 8 Apr 26, 1832H

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