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Magazine Chapter 1: Q 41. (page 43)
Dates on coins
(a) Sketch a dot-plot for a distribution that is skewed to the left.
(b) Suppose that you and your friends emptied your pockets of coins and recorded the year marked on each coin. The distribution of dates would be skewed to the left. Explain why.
Short Answer
Part (b) The distribution is skewed towards the left because most of the coins were of recent manufacture year.
Part (a) the dot- plot is
Step by step solution
Given information
Assume you and your friends emptied your pockets of coins and jotted down the year on each one. The dates are tilted to the left in their distribution.
Part (a) Step 2: Concept
Drawing the number line by placing the dots in given values on the number line. The numbers need to be in the center and a few dots need to be on the left.
Part (a) Step 3: Explanation
Student's marks in the statistical subject are given below:
| Marks in statistic | Frequency |
| 12 | 1 |
| 13 | 1 |
| 15 | 1 |
| 16 | 1 |
| 17 | 1 |
| 17 | 2 |
| 1 | 1 |
| 18 | 2 |
| 18 | 1 |
| 19 | 3 |
| 19 | 2 |
| 19 | 1 |
| 20 | 4 |
| 20 | 3 |
| 20 | 2 |
| 20 | 1 |
| 21 | 10 |
| 21 | 9 |
| 21 | 8 |
| 21 | 7 |
| 21 | 6 |
| 21 | 5 |
| 21 | 4 |
| 21 | 3 |
| 21 | 2 |
| 21 | 1 |
| 22 | 7 |
| 22 | 6 |
| 22 | 5 |
| 22 | 4 |
| 22 | 3 |
| 22 | 2 |
| 22 | 1 |
| 23 | 3 |
| 23 | 2 |
| 23 | 1 |
The above-mentioned dot plot is tilted to the left:
Therefore, the dot plot for distribution is plotted.
Part (b) Step 1: Explanation
We can do a dating experiment here by documenting the years marked on each coin from the pockets of two people.
| Year | Frequency |
| 1991 | 1 |
| 1991 | 2 |
| 2001 | 1 |
| 2001 | 2 |
| 2001 | 3 |
| 2002 | 1 |
| 2002 | 2 |
| 2003 | 1 |
| 2005 | 1 |
| 2005 | 2 |
| 2005 | 3 |
| 2005 | 4 |
| 2008 | 1 |
| 2008 | 2 |
| 2010 | 1 |
| 2011 | 1 |
| 2011 | 2 |
| 2011 | 3 |
| 2011 | 4 |
| 2011 | 5 |
The dot pot is given below:
Because the majority of the coins were manufactured recently, the distribution is skewed to the left.
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