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\n" ); document.write( "Part (i)\r
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\n" ); document.write( "\n" ); document.write( "Original table
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| Marks | Number of students |
| 40-44 | 7 |
| 45-49 | 10 |
| 50-54 | 20 |
| 55-59 | f4 |
| 60-64 | f5 |
| 65-69 | 6 |
| 70-74 | 3 |
\n" ); document.write( "Spreadsheet software is strongly recommended.\r
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\n" ); document.write( "\n" ); document.write( "20% of 75 = 0.20*75 = 15 students have marks between 55 and 59.
\n" ); document.write( "This means f4 = 15.\r
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\n" ); document.write( "\n" ); document.write( "Add up the frequencies in the 2nd column.
\n" ); document.write( "Set this sum equal to 75 so we can determine the value of f5.
\n" ); document.write( "7+10+20+f4+f5+6+3 = 75
\n" ); document.write( "7+10+20+15+f5+6+3 = 75
\n" ); document.write( "61+f5 = 75
\n" ); document.write( "f5 = 75-61
\n" ); document.write( "f5 = 14\r
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\n" ); document.write( "\n" ); document.write( "Part (ii)\r
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\n" ); document.write( "\n" ); document.write( "In the previous part we found that
\n" ); document.write( "f4 = 15 and f5 = 14\r
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\n" ); document.write( "\n" ); document.write( "After replacing f4 and f5 with those values, we now have this grouped frequency table.
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| Marks | Number of students |
| 40-44 | 7 |
| 45-49 | 10 |
| 50-54 | 20 |
| 55-59 | 15 |
| 60-64 | 14 |
| 65-69 | 6 |
| 70-74 | 3 |
\n" ); document.write( "Let's introduce a new column which I'll refer to as column m.
\n" ); document.write( "m = midpoint of the corresponding class interval
\n" ); document.write( "To find the midpoint, add the endpoints and divide by 2.
\n" ); document.write( "Example: m = 42 for the first class since (40+44)/2 = 42\r
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\n" ); document.write( "\n" ); document.write( "Here's what the table looks like now
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| Marks | Number of students | m |
| 40-44 | 7 | 42 |
| 45-49 | 10 | 47 |
| 50-54 | 20 | 52 |
| 55-59 | 15 | 57 |
| 60-64 | 14 | 62 |
| 65-69 | 6 | 67 |
| 70-74 | 3 | 72 |
\n" ); document.write( "The midpoint is the best representative mark from each class interval.
\n" ); document.write( "Multiply the frequency value (f) with its corresponding midpoint (m).
\n" ); document.write( "This will form a new column which I'll label as f*m.
\n" ); document.write( "For example, f*m = 7*42 = 294 is the first item in this new column.\r
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| Marks | Number of students | M = midpoint | f*m |
| 40-44 | 7 | 42 | 294 |
| 45-49 | 10 | 47 | 470 |
| 50-54 | 20 | 52 | 1040 |
| 55-59 | 15 | 57 | 855 |
| 60-64 | 14 | 62 | 868 |
| 65-69 | 6 | 67 | 402 |
| 70-74 | 3 | 72 | 216 |
\n" ); document.write( "Add up the values in this new column to get
\n" ); document.write( "294+470+1040+855+868+402+216 = 4145\r
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\n" ); document.write( "\n" ); document.write( "Then divide this over the total number of people (75) to get 4145/75 = 55.266667 which is the approximate mean.
\n" ); document.write( "The 6's go on forever but we have to round at some point.\r
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\n" ); document.write( "\n" ); document.write( "Answers:
- f4 = 15 and f5 = 14
- mean = 55.266667 approximately
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