Question

calculate mean ,median and mode from the following : marks less than - 10 20 30 40 50 60 70 80 no.of students 12 16 27 48 90 106 122 150​

Answer 1

Answer:

For calculating the Mean, Median and Mode of the following above given data, let us first calculate certain information from the table in the figure attached below:

Mean of the data:

∴ Mean = ∑(f*m) / N

⇒ Mean = 31715 / 571 = 55.54

Median of the data:

Median = L + [(N/2 – c) / f] * i

Here,  

N/2 = 571/2 = 285.5  

Median class = 50-60

L = 50 = lower limit of the median class  

c = 193 = previous cumulative frequency

f = 106 = frequency of the particular median class

i = 10 = interval of marks

∴ Median = 50 + [(285.5 - 193) / 106] * 10 = 50 + 8.72 = 58.72

Mode of the data:

Mode = L + [(f1-fo) / (2f1 – fo – f2)] * h

Here,

f1 = 150 = maximum frequency of the modal class

L = 70 = lower limit of the modal class

h = 10 = size of the class interval

fo = 122 = frequency of the class preceding the modal class

f2 = no value = frequency of the class succeeding the modal class

Since the frequency of the modal class is the last value of frequency given in the data table, so there is no value for the frequency of the class succeeding the modal class i.e., f2, therefore, there will be no mode for the given data.