Recently the half-yearly examination was conducted in DAV public … - Vidyadip

Question

Recently the half-yearly examination was conducted in DAV public school. The mathematics teacher maintains a record of the marks of 100 students. On the basis of the recorded data of the marks obtained in Mathematics, the histogram is given below:

The construction of the cumulative frequency table is useful in determining the...
Identify the modal class from the given graph are?
Find the mode of the distribution of marks obtained by the students in an examination.
Or
Given the mean of the above distribution is 53, using empirical relationship estimate the value of its median.

✓

Answer

1. Median = 582. Here, maximum frequency is 29 and it belongs to class 60-80, so Modal class = 60-80(c) Modal class is the class having maximum number of frequency.
3. Mode $=\text{l}+\frac{\text{f}_1-\text{f}_0}{0\text{f}_1-\text{f}_0-\text{f}_2}\times\text{h}$
Here, $l = 60, f_1= 29, f_0= 21, f_2= 17$ and $h = 20$
Mode $=60+\frac{29-21}{2\times29-21-17}\times20$
$=60+\frac{8}{58-38}\times20=68$
Or
Mode = 3 median - 2 mean
Mode = 68 and mean = 53 (given)
$\therefore$ 3 median = mode + 2 mean
Median = 68 + 2 × 53
Median $=\frac{174}3=58$
Hence, Median = 58

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