Name: Mean of Ungrouped data: Example
Uploaded: 2019-07-19
Duration: 2 min 7 s
Description: Familiarise yourself with the calculation of the arithmetic means of the values collected in the data. This example involves marks scored by students.

Question

Find the mean, median and the mode of the following data:

Weight (in $Kg$ )	$42$	$47$	$52$	$57$	$62$	$67$	$72$
Number of persons	$3$	$8$	$6$	$8$	$11$	$5$	$9$

Accepted Answer

Given:

Weight (in $Kg$ ) $42$ $47$ $52$ $57$ $62$ $67$ $72$

Number of persons $3$ $8$ $6$ $8$ $11$ $5$ $9$

To calculate the mean, median and mode:

Weight
(in $Kg$ )

$x_{i}$

Number of persons

$F_{i}$

Cumulative frequency
$x_{i} F_{i}$

$42$ $3$ $3$ $126$

$47$ $8$ $11$ $376$

$52$ $6$ $17$ $312$

$57$ $8$ $25$ $456$

$62$ $11$ $36$ $682$

$67$ $5$ $41$ $335$

$72$ $9$ $50$ $648$

Total $Σ_{F_{i}} = 50$ $Σ_{x_{i} F_{i}} = 2935$

Mean $=$ $\frac{Σ_{x_{i} F_{i}}}{Σ_{F_{i}}} = \frac{2935}{50} = 58.7 Kg$

Here the total number of observations $(n) = 50$

$Median = \frac{1}{2} [value of {(\frac{n}{2})}^{th} term + value of {(\frac{n}{2} + 1)}^{th} term] Median = \frac{1}{2} [value of 25^{th} term + value of 26^{th} term] Median = \frac{1}{2} [57 + 62] = \frac{119}{2} = 59.5 Kg$

The highest frequency is $11$ and the corresponding value of $x_{i}$ for the frequency $11$ is $62$ .

Therefore, the mode is $62$ .

Hence, the mode is $62 Kg$ , median is $59.5 Kg$ and the mean is $58.7 Kg$ .

Weight (in $kg$ )	$48$	$50$	$52$	$54$	$58$
Number of players	$4$	$3$	$2$	$2$	$1$

Find the mean, median and the mode of the following data:

Weight (in $Kg$ ) $42$ $47$ $52$ $57$ $62$ $67$ $72$

Number of persons $3$ $8$ $6$ $8$ $11$ $5$ $9$

Important Questions on Statistics

Learn and Prepare for any exam you want !

Find the mean, median and the mode of the following data: Weight (in Kg) 42 47 52 57 62 67 72 Number of persons 3 8 6 8 11 5 9

Important Questions on Statistics

Learn and Prepare for any exam you want !

Find the mean, median and the mode of the following data:

Weight (in $Kg$ ) $42$ $47$ $52$ $57$ $62$ $67$ $72$

Number of persons $3$ $8$ $6$ $8$ $11$ $5$ $9$