Question

The following is the record of marks of 40 candidates in the Mathematics assessment 65 84 91 58 43 86 73 33 76 80 57 33 53 29 40 27 72 19 51 67 37 14 18 92 13 45 61 39 23 22 22 41 27 51 63 47 19 35 39 76 Using a class interval 11-20, 21-30,… construct a Frequency Distribution table and find the Median and Mode of the distribution.

Answer 1

The median of the given data is 46.5 and the mode is 41.5

Given:-

The records of 40 candidates

To Find:-

$Median=l+\frac{h}{f}(\frac{N}{2}-c)$

Mode

Where,l = lower class boundaries of the median class

h=size of the median class

f=frequency of the median class

N=Total number of observations

c=Cumulative frequency of the median class

Solution:-

i) To find the median, we first need to find the median class which is the total cumulative frequency divided by 2.

⇒N/2=40/2

N/2=20

∴The class which is closest and greater to 20 is 40.5-50.5 which has a frequency of 22.

$Median=l+\frac{h}{f}(\frac{N}{2}-c)$

$Median=40.5+\frac{10}{5}(\frac{40}{2}-17)$

$Median=40.5+2(20-17)$

Median = 46.5

ii) To find mode, we need to find the modal class which is the class with the highest frequency. In this data, however, we have two classes with the highest frequency i.e. 20.5-30.5 and 30.5-40.5. Thus, our data is binomial, so our formula is,

Mode = 3 Median - 2 Mean

To find the mean, we use the formula,

Mean = ∑fm/∑f

Mean=1960/40

Mean=49

∴Mode = 3(46.5) - 2(49)

Mode = 139.5-98

Mode=41.5

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