Maths Case study (4 Marks)

100m Race
A stopwatch was used to find the time that it took a group of students to run 100m.

Time (in sec)	0-10	10-20	20-30	30-40	40-50
No. of students	4	11	14	5	6

1. The construction of cummulative frequency table is useful in determining the:
2. Estimate the mean time taken by a student to finish the race:
3. What wiil be the lower limit of the modal class?
   Or
   The sum of upper limits of median class and modal class is:

Marks obtained by 40 students of a class-10 in an examination. Out of 50 are given below:

Marks	0-10	10-20	20-30	30-40	40-50
No. of Students	3	11	9	12	5

1. While computing mean of a grouped data, we assume that the frequencies are:
2. What will be the upper limit of the median class?
3. The sum of lower limit of model class and upper limit of median class is:
   Or
   Estimate the mean marks obtain by a student:

The DAV public school organized a free health check-up camp for the 60 students of class 10th. They have provided the BMI report to each student. This report estimates the body fat and is a good measure of risk for diseases that can occur with overweight and obesity. On the basis of this report, the following graph is made which describes the weight (in kg) of the students:

1. The empirical relationship between mean, median and mode is:
2. Identify the modal class in the given graph.
3. Calculate the mode weight of the students.
   Or
   Find the median weight of the students if the mean weight is 55.2 kg.

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:

1. The construction of the cumulative frequency table is useful in determining the...
2. Identify the modal class from the given graph are?
3. 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.

On a paricular day, National Highway Authority of india (NHAI) Checked the toll tax collection of a particular toll plaza in rajasthan.

The following table shows the toll tax paid by drivers and the number of vehicles on that particular day.

Toll tax (in ₹)	30-40	40-50	50-60	60-70	70-80
Number of vehicles	80	100	120	70	40

Based on the above information, answer the following questions.

1. The mean of toll tax received by NHAI by direct method is?
2. If A is taken as assumed mean, then the possible value of A is?
3. The mean of toll tax received by NHAI by assumed mean method is?
   Or
   The average toll tax received by NHAI in a day, from that particular toll plaza, is?