The distances (in $km$) of $40$ engineers from their residence to their place of work were found as follows:
$5$ $3$ $10$ $20$ $25$ $11$ $13$ $7$ $12$ $31$ $19$ $10$ $12$ $17$ $18$ $11$ $32$ $17$ $16$ $2$ $7$ $9$ $7$ $8$ $3$ $5$ $12$ $15$ $18$ $3$ $12$ $14$ $2$ $9$ $6$ $15$ $15$ $7$ $6$ $12$
Construct a grouped frequency distribution table with class size $5$ for the data given above,taking the first interval as $0-5$ ($5$ not included). What main features do you observe from this tabular representation?
| $5$ | $3$ | $10$ | $20$ | $25$ | $11$ | $13$ | $7$ | $12$ | $31$ |
| $19$ | $10$ | $12$ | $17$ | $18$ | $11$ | $32$ | $17$ | $16$ | $2$ |
| $7$ | $9$ | $7$ | $8$ | $3$ | $5$ | $12$ | $15$ | $18$ | $3$ |
| $12$ | $14$ | $2$ | $9$ | $6$ | $15$ | $15$ | $7$ | $6$ | $12$ |
Construct a grouped frequency distribution table with class size $5$ for the data given above,taking the first interval as $0-5$ ($5$ not included). What main features do you observe from this tabular representation?
(N/A) To construct a grouped frequency distribution table with a class size of $5$,we use intervals: $0-5, 5-10, 10-15, 15-20, 20-25, 25-30, 30-35$.
Observations:
$1$. Most of the engineers (i.e.,$5+11+11+9 = 36$ engineers) live within a distance of $20\, km$ from their workplace.
$2$. Very few engineers (i.e.,$1+1+2 = 4$ engineers) live at a distance of $20\, km$ or more from their workplace.
| Distance (in $km$) | Number of engineers |
| $0-5$ | $5$ |
| $5-10$ | $11$ |
| $10-15$ | $11$ |
| $15-20$ | $9$ |
| $20-25$ | $1$ |
| $25-30$ | $1$ |
| $30-35$ | $2$ |
| Total | $40$ |
Observations:
$1$. Most of the engineers (i.e.,$5+11+11+9 = 36$ engineers) live within a distance of $20\, km$ from their workplace.
$2$. Very few engineers (i.e.,$1+1+2 = 4$ engineers) live at a distance of $20\, km$ or more from their workplace.
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