Q) Activities like running or cycling reduce stress and the risk of mental disorders like depression. Running helps build endurance. Children develop stronger bones and muscles and are less prone to gain weight.

The physical education teacher of a school has decided to conduct an interschool running tournament in his school premises. The time taken by a group of students to run 100 m, was noted as follows :

Based on the above, answer the following questions :
(i) What is the median class of the above given data?
(ii) Find the mean time taken by the students to finish the race.
(iii) Find the mode of the above given data.
(iv) How many students took time less than 60 seconds?

Ans:

(i) Median class of data:

To calculate the median value, let’s re-organize the data:

To find the median, we need to first identify middle class of the data.

• We know that, Median class is the class where the cumulative frequency crosses 50% of total of frequencies.
• Here, in the given data, total of frequencies is 40 and at row 3, cumulative frequency 31 is crossing 50% of total (i.e. 20)
• Hence, our Median class = 40-60

(ii) Mean Value of data:

To calculate the mean value, let’s re-organize the data:

To arrange the above, we take following steps:

• We calculate midpoint ‘x’ of each class by
• Then we calculate ‘fx’ by multiplying midpoint of each class with frequency of that class
• We calculate Σf by summing up all the frequencies and Σfx by adding up all the values of fx

Next, we know that, mean of grouped data is given by:

Mean of grouped data =

Therefore, Mean value = = 47.50

Hence, the mean value of the given data is 47.50

(iii) Mode value of the data:

Let’s relook at the given data:

Since the modal class is the class with the highest frequency.

In the given question, class “40 – 60” has frequency of 13 which is the highest frequency among all other classes.

Hence, modal class is “40 – 60”.

Now mode of the grouped data is calculated by:

Mode = L + x h

Here,

L = lower class limit of modal class = 40

 = frequency of modal class = 13

 = frequency of class proceeding to modal class = 10

 = frequency of class succeeding to modal class = 6

h = class size = 60 – 40 = 20

Let’s put values in the formula and solve:

Mode = L + x h

= 40 + x 20

= 40 + x 20

= 40 + 6 = 46.0

Hence, the mode value is 46.0

(iv) students taking less than 60 seconds:

Let’s relook at the given data:

Students taken time less than 60 students = Students taken time from 0 – 20 seconds + Students taken time 20 -40 seconds + Students taken time 40 – 60 seconds

=  8 + 10 + 13 = 31

Therefore 31 students took time less than 60 seconds.

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