Question 13 Marks
The weights (in kg.) of $15$ students of a class are $:38, 42, 35, 37, 45, 50, 32, 43, 43, 40, 36, 38, 43, 38, 47. (i) $ Find the mode and median of this data.$(ii)$ Is there more than one mode$ ?$
Answer$(i)$ For Median. We arrange the data in ascending order, we get
$32, 35, 36, 37, 38, 38, 38, 40, 42, 43, 43, 43, 48, 47, 50$
Median is the middle observation.
Therefore, $40\ kg$ is the median.
For Mode. Mode $=$ observation with highest frequency
$= 38\ kg$ and $43\ kg$
$(ii)$ Yes ! there are $2 ($more than one$)$ modes.
View full question & answer→Question 23 Marks
The runs scored in a cricket match by $11$ players is as follows: $6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15.$ Find the mean, mode and median of this data. Are the three same$?$
Answer$i.$ For mean
Mean $= \frac{\text { Sum of all observations }}{\text { number of observations }}$
$= \frac{6+15+120+50+100+80+10+15+8+10+15}{11}$
$= \frac{429}{11} $
$= 39$
$ii.$ For Median
We arrange the data in ascending order, we get
$6, 8, 10, 10, 15, 15, 15, 50, 80, 100, 120$
Median is the middle observation. Therefore, $15$ is the median.
$iii.$ For Mode
Mode $=$ observation with highest frequency $= 15$
No! They are not the same.
View full question & answer→Question 33 Marks
The margins of victory in the football matches of a league are:
$1, 3, 2, 5, 1, 4, 6, 2, 5, 2, 2, 2, 4, 1, 2, 3, 1, 1, 2, 3, 2, 6, 4, 3, 2, 1, 1, 4, 2, 1, 5, 3, 3, 2, 3, 2, 4, 2, 1, 2$
Find the mode of this data.
AnswerLet us put the data in a tabular form as shown below:
| Margins of Victory |
Tally Bars |
Number of Matches |
| $1$ |
 $|||||||||$ |
$9$ |
| $2$ |
  $||||$ |
$14$ |
| $3$ |
 $||$ |
$7$ |
| $4$ |
 |
$5$ |
| $5$ |
$|||$ |
$3$ |
| $6$ |
$||$ |
$2$ |
| |
Total |
$40$ |
Looking at the table, it can be easily said that $2$ is the ‘mode’ as $2$ has occurred the highest number of times in the above table. Thus, most of the matches have been won with a victory margin of $2$ goals. View full question & answer→